dataset_name stringclasses 1
value | task stringclasses 9
values | case stringclasses 44
values | prompt stringlengths 799 6.65k | answer stringlengths 1 486 | nodes stringclasses 23
values | edges stringlengths 72 991 | direction stringclasses 2
values | samples stringclasses 91
values | name_to_id_mapping stringlengths 119 626 | source_file stringclasses 1
value | answer_type stringclasses 2
values |
|---|---|---|---|---|---|---|---|---|---|---|---|
real_erdos | dominating_set | critical_infrastructure | We're planning emergency shutdown controls for an industrial complex. Facilities are: Substation_1, Police_Station_West, City_Hall, Defense_Installation_1, Nuclear_Facility_Checkpoint, Bridge_Control_A, Tunnel_Entrance_2, Pumping_Station_A, Police_Station_East, Satellite_Ground_Station, Medical_Supply_Center, Tunnel_En... | ["Substation_1", "Tunnel_Entrance_2", "Pumping_Station_A", "Satellite_Ground_Station", "Hospital_Main", "Government_Building_A"] | (0, 20) | [[0, 1], [0, 2], [0, 3], [0, 4], [0, 5], [0, 13], [0, 16], [1, 4], [1, 5], [1, 6], [1, 7], [1, 8], [1, 9], [1, 10], [1, 11], [1, 12], [1, 14], [1, 15], [3, 4], [3, 7], [3, 11], [3, 14], [3, 15], [4, 5], [4, 6], [4, 7], [4, 8], [4, 9], [4, 12], [4, 13], [4, 16], [5, 6], [5, 9], [5, 10], [5, 16], [5, 18], [6, 8], [6, 10]... | undirected | none | {"Substation_1": "0", "Police_Station_West": "1", "City_Hall": "2", "Defense_Installation_1": "3", "Nuclear_Facility_Checkpoint": "4", "Bridge_Control_A": "5", "Tunnel_Entrance_2": "6", "Pumping_Station_A": "7", "Police_Station_East": "8", "Satellite_Ground_Station": "9", "Medical_Supply_Center": "10", "Tunnel_Entrance... | none | node_list |
real_erdos | dominating_set | critical_infrastructure | We're planning emergency shutdown controls for an industrial complex. Facilities are: Seismic_Monitor_A, Weather_Station_Central, Power_Plant_B, Command_Center_North, Government_Building_A, Water_Treatment_Facility, Gas_Distribution_Center, Emergency_Operations_Center, Pumping_Station_B, Military_Base_Alpha, Airport_Te... | ["Seismic_Monitor_A", "Weather_Station_Central", "Power_Plant_B", "Water_Treatment_Facility", "Pumping_Station_B", "Bridge_Control_A", "Hospital_Emergency"] | (0, 19) | [[0, 6], [0, 7], [0, 10], [0, 12], [0, 13], [0, 15], [0, 18], [1, 4], [1, 9], [1, 17], [2, 3], [2, 9], [2, 10], [2, 15], [2, 16], [3, 5], [3, 6], [3, 8], [3, 10], [3, 12], [3, 16], [4, 5], [4, 9], [4, 16], [4, 18], [5, 12], [5, 13], [5, 15], [5, 16], [5, 18], [6, 9], [6, 18], [7, 9], [7, 11], [8, 16], [9, 11], [9, 17],... | undirected | none | {"Seismic_Monitor_A": "0", "Weather_Station_Central": "1", "Power_Plant_B": "2", "Command_Center_North": "3", "Government_Building_A": "4", "Water_Treatment_Facility": "5", "Gas_Distribution_Center": "6", "Emergency_Operations_Center": "7", "Pumping_Station_B": "8", "Military_Base_Alpha": "9", "Airport_Terminal": "10",... | none | node_list |
real_erdos | dominating_set | critical_infrastructure | We're planning emergency shutdown controls for an industrial complex. Facilities are: Bridge_Control_A, Government_Building_A, Nuclear_Facility_Checkpoint, Railway_Hub, Emergency_Shelter_1, Gas_Distribution_Center, City_Hall, Military_Base_Alpha, Food_Distribution_Hub, Emergency_Shelter_2, Fire_Station_North, Oil_Refin... | ["Bridge_Control_A", "Gas_Distribution_Center", "Military_Base_Alpha", "Fire_Station_North"] | (0, 13) | [[0, 1], [0, 2], [0, 3], [0, 4], [0, 6], [0, 8], [0, 9], [0, 12], [1, 7], [1, 10], [2, 4], [2, 6], [2, 10], [2, 12], [3, 6], [3, 7], [3, 9], [3, 11], [4, 9], [4, 10], [4, 11], [4, 12], [5, 6], [6, 7], [6, 12], [7, 8], [9, 11], [10, 11]] | undirected | none | {"Bridge_Control_A": "0", "Government_Building_A": "1", "Nuclear_Facility_Checkpoint": "2", "Railway_Hub": "3", "Emergency_Shelter_1": "4", "Gas_Distribution_Center": "5", "City_Hall": "6", "Military_Base_Alpha": "7", "Food_Distribution_Hub": "8", "Emergency_Shelter_2": "9", "Fire_Station_North": "10", "Oil_Refinery_A"... | none | node_list |
real_erdos | dominating_set | critical_infrastructure | A power grid requires monitoring stations for failure detection. Grid nodes: Oil_Refinery_A, Communication_Tower_A, Hospital_Emergency, Food_Distribution_Hub, Police_Station_West, Data_Exchange_Point, Fire_Station_North, Command_Center_North, Military_Base_Alpha, Dam_Control_Station, Power_Plant_A, Airport_Terminal, Me... | ["Oil_Refinery_A", "Hospital_Emergency", "Food_Distribution_Hub", "Police_Station_West", "Data_Exchange_Point", "Fire_Station_North", "Power_Plant_A"] | (0, 19) | [[0, 1], [0, 8], [0, 9], [0, 16], [1, 7], [1, 8], [1, 12], [1, 17], [2, 16], [2, 17], [3, 8], [3, 13], [3, 14], [3, 18], [4, 13], [4, 15], [4, 16], [5, 7], [5, 12], [5, 15], [5, 16], [6, 11], [6, 13], [6, 16], [7, 10], [7, 11], [7, 15], [8, 15], [8, 18], [9, 13], [9, 17], [9, 18], [10, 11], [10, 12], [10, 13], [10, 17]... | undirected | none | {"Oil_Refinery_A": "0", "Communication_Tower_A": "1", "Hospital_Emergency": "2", "Food_Distribution_Hub": "3", "Police_Station_West": "4", "Data_Exchange_Point": "5", "Fire_Station_North": "6", "Command_Center_North": "7", "Military_Base_Alpha": "8", "Dam_Control_Station": "9", "Power_Plant_A": "10", "Airport_Terminal"... | none | node_list |
real_erdos | dominating_set | critical_infrastructure | A city needs to place security cameras to monitor critical infrastructure. The infrastructure nodes are: Command_Center_North, Emergency_Operations_Center, Hospital_Main, Airport_Terminal, Power_Plant_B, Medical_Supply_Center, Bridge_Control_B, Gas_Distribution_Center, Substation_3, Substation_2, Pumping_Station_A, Rai... | ["Command_Center_North", "Substation_3", "Satellite_Ground_Station", "Nuclear_Facility_Checkpoint"] | (0, 20) | [[0, 1], [0, 2], [0, 3], [0, 4], [0, 5], [0, 6], [0, 7], [0, 9], [0, 10], [0, 11], [0, 12], [0, 13], [0, 17], [0, 18], [0, 19], [1, 10], [1, 12], [2, 4], [2, 8], [2, 9], [2, 11], [2, 16], [3, 4], [3, 5], [3, 19], [4, 5], [4, 6], [4, 7], [5, 6], [5, 8], [5, 9], [5, 10], [5, 11], [5, 13], [5, 14], [5, 15], [5, 18], [6, 7... | undirected | none | {"Command_Center_North": "0", "Emergency_Operations_Center": "1", "Hospital_Main": "2", "Airport_Terminal": "3", "Power_Plant_B": "4", "Medical_Supply_Center": "5", "Bridge_Control_B": "6", "Gas_Distribution_Center": "7", "Substation_3": "8", "Substation_2": "9", "Pumping_Station_A": "10", "Railway_Hub": "11", "Tunnel_... | none | node_list |
real_erdos | dominating_set | critical_infrastructure | A city needs to place security cameras to monitor critical infrastructure. The infrastructure nodes are: Military_Base_Alpha, Emergency_Operations_Center, Satellite_Ground_Station, Defense_Installation_1, Railway_Hub, Bus_Depot_Central, Hospital_Main, Emergency_Shelter_2, Gas_Distribution_Center, Port_Authority, Weathe... | ["Military_Base_Alpha", "Bus_Depot_Central", "Hospital_Main", "Gas_Distribution_Center", "Port_Authority", "Weather_Station_Central", "Reservoir_Facility", "Food_Distribution_Hub"] | (0, 19) | [[0, 1], [0, 2], [0, 3], [0, 4], [0, 14], [0, 15], [0, 16], [1, 5], [1, 6], [1, 8], [2, 3], [2, 4], [2, 5], [2, 7], [2, 8], [2, 9], [3, 10], [3, 18], [4, 6], [4, 9], [4, 10], [4, 11], [4, 12], [4, 13], [4, 17], [5, 7], [8, 11], [8, 13], [9, 14], [9, 15], [10, 12], [12, 16], [15, 17], [16, 18]] | undirected | none | {"Military_Base_Alpha": "0", "Emergency_Operations_Center": "1", "Satellite_Ground_Station": "2", "Defense_Installation_1": "3", "Railway_Hub": "4", "Bus_Depot_Central": "5", "Hospital_Main": "6", "Emergency_Shelter_2": "7", "Gas_Distribution_Center": "8", "Port_Authority": "9", "Weather_Station_Central": "10", "Govern... | none | node_list |
real_erdos | dominating_set | critical_infrastructure | A city needs to place security cameras to monitor critical infrastructure. The infrastructure nodes are: Tunnel_Entrance_2, Emergency_Operations_Center, Fire_Station_North, Gas_Distribution_Center, Water_Treatment_Facility, Fire_Station_Central, Strategic_Reserve_Site, Police_Headquarters, Substation_3, Oil_Refinery_A,... | ["Tunnel_Entrance_2", "Gas_Distribution_Center", "Water_Treatment_Facility", "Strategic_Reserve_Site", "Police_Headquarters", "Power_Plant_A"] | (0, 14) | [[0, 1], [0, 2], [0, 5], [1, 4], [1, 5], [1, 10], [1, 13], [2, 9], [2, 10], [2, 12], [3, 5], [3, 8], [3, 9], [4, 10], [5, 12], [6, 11], [7, 10], [7, 12], [8, 10], [8, 11], [8, 13], [9, 12], [10, 11], [11, 13]] | undirected | none | {"Tunnel_Entrance_2": "0", "Emergency_Operations_Center": "1", "Fire_Station_North": "2", "Gas_Distribution_Center": "3", "Water_Treatment_Facility": "4", "Fire_Station_Central": "5", "Strategic_Reserve_Site": "6", "Police_Headquarters": "7", "Substation_3": "8", "Oil_Refinery_A": "9", "City_Hall": "10", "Bridge_Contro... | none | node_list |
real_erdos | dominating_set | critical_infrastructure | We're planning emergency shutdown controls for an industrial complex. Facilities are: Strategic_Reserve_Site, Emergency_Operations_Center, Hospital_Main, Substation_1, Airport_Terminal, Fire_Station_Central, Pumping_Station_A, Medical_Supply_Center, Bridge_Control_B, Telecommunications_Hub_A, Power_Plant_A, Railway_Hub... | ["Strategic_Reserve_Site", "Emergency_Operations_Center", "Hospital_Main", "Substation_1", "Pumping_Station_A"] | (0, 12) | [[0, 4], [0, 8], [1, 4], [1, 9], [1, 11], [2, 5], [2, 8], [2, 10], [3, 4], [3, 7], [3, 11], [4, 5], [5, 6], [5, 7], [6, 9], [6, 11]] | undirected | none | {"Strategic_Reserve_Site": "0", "Emergency_Operations_Center": "1", "Hospital_Main": "2", "Substation_1": "3", "Airport_Terminal": "4", "Fire_Station_Central": "5", "Pumping_Station_A": "6", "Medical_Supply_Center": "7", "Bridge_Control_B": "8", "Telecommunications_Hub_A": "9", "Power_Plant_A": "10", "Railway_Hub": "11... | none | node_list |
real_erdos | dominating_set | critical_infrastructure | We're planning emergency shutdown controls for an industrial complex. Facilities are: Pumping_Station_A, Substation_3, Substation_1, Nuclear_Facility_Checkpoint, Bus_Depot_Central, Pumping_Station_B, Food_Distribution_Hub, Emergency_Shelter_1, Chemical_Plant_B, Emergency_Operations_Center, Satellite_Ground_Station, Air... | ["Pumping_Station_A", "Substation_3", "Substation_1", "Bus_Depot_Central", "Pumping_Station_B", "Emergency_Shelter_1", "Satellite_Ground_Station"] | (0, 13) | [[0, 3], [0, 6], [0, 12], [1, 9], [1, 11], [2, 8], [3, 7], [3, 11], [4, 12], [5, 12], [6, 11], [6, 12], [7, 9], [8, 11], [9, 12], [10, 11], [10, 12], [11, 12]] | undirected | none | {"Pumping_Station_A": "0", "Substation_3": "1", "Substation_1": "2", "Nuclear_Facility_Checkpoint": "3", "Bus_Depot_Central": "4", "Pumping_Station_B": "5", "Food_Distribution_Hub": "6", "Emergency_Shelter_1": "7", "Chemical_Plant_B": "8", "Emergency_Operations_Center": "9", "Satellite_Ground_Station": "10", "Airport_T... | none | node_list |
real_erdos | dominating_set | critical_infrastructure | A power grid requires monitoring stations for failure detection. Grid nodes: Power_Plant_B, Emergency_Shelter_2, Communication_Tower_A, Command_Center_North, Tunnel_Entrance_1, Fire_Station_North, Water_Treatment_Facility, Railway_Hub, Substation_1, Police_Station_East, Telecommunications_Hub_B, Pumping_Station_A, Nucl... | ["Power_Plant_B", "Emergency_Shelter_2", "Communication_Tower_A", "Command_Center_North", "Water_Treatment_Facility"] | (0, 16) | [[0, 4], [0, 5], [0, 7], [0, 10], [0, 13], [1, 4], [1, 5], [1, 8], [1, 9], [2, 5], [2, 7], [2, 8], [3, 5], [3, 8], [3, 10], [3, 12], [3, 14], [4, 9], [4, 10], [4, 12], [4, 13], [5, 6], [5, 9], [5, 10], [5, 11], [6, 8], [6, 11], [6, 15], [7, 8], [7, 9], [7, 12], [8, 12], [8, 14], [9, 12], [10, 12], [11, 13], [11, 14], [... | undirected | none | {"Power_Plant_B": "0", "Emergency_Shelter_2": "1", "Communication_Tower_A": "2", "Command_Center_North": "3", "Tunnel_Entrance_1": "4", "Fire_Station_North": "5", "Water_Treatment_Facility": "6", "Railway_Hub": "7", "Substation_1": "8", "Police_Station_East": "9", "Telecommunications_Hub_B": "10", "Pumping_Station_A": ... | none | node_list |
real_erdos | dominating_set | critical_infrastructure | We're planning emergency shutdown controls for an industrial complex. Facilities are: Police_Station_West, Pumping_Station_B, Military_Base_Alpha, Tunnel_Entrance_2, Weather_Station_Central, Bus_Depot_Central, City_Hall, Pumping_Station_A, Port_Authority, Bridge_Control_A, Chemical_Plant_B, Communication_Tower_A, Airpo... | ["Police_Station_West", "Pumping_Station_B", "City_Hall", "Port_Authority", "Airport_Terminal"] | (0, 18) | [[0, 2], [0, 3], [0, 4], [0, 5], [0, 11], [0, 13], [0, 14], [0, 16], [0, 17], [1, 5], [1, 7], [1, 9], [1, 10], [1, 11], [2, 5], [2, 8], [2, 10], [2, 11], [2, 14], [2, 16], [2, 17], [3, 8], [3, 9], [3, 13], [3, 17], [4, 5], [4, 7], [4, 8], [4, 11], [4, 13], [4, 16], [5, 7], [5, 8], [5, 12], [5, 15], [6, 11], [6, 13], [6... | undirected | none | {"Police_Station_West": "0", "Pumping_Station_B": "1", "Military_Base_Alpha": "2", "Tunnel_Entrance_2": "3", "Weather_Station_Central": "4", "Bus_Depot_Central": "5", "City_Hall": "6", "Pumping_Station_A": "7", "Port_Authority": "8", "Bridge_Control_A": "9", "Chemical_Plant_B": "10", "Communication_Tower_A": "11", "Air... | none | node_list |
real_erdos | dominating_set | critical_infrastructure | You're designing a disaster resilience system for urban infrastructure. Critical facilities include: Substation_2, Defense_Installation_1, Strategic_Reserve_Site, Water_Treatment_Facility, Nuclear_Facility_Checkpoint, Oil_Refinery_A, Tunnel_Entrance_1, Hospital_Emergency, Weather_Station_Central, Fire_Station_Central, ... | ["Substation_2", "Oil_Refinery_A", "Tunnel_Entrance_1", "Hospital_Emergency", "Gas_Distribution_Center", "Emergency_Shelter_1", "Emergency_Shelter_2", "Military_Base_Alpha"] | (0, 20) | [[0, 1], [0, 2], [0, 3], [0, 4], [0, 8], [0, 10], [0, 13], [0, 14], [0, 17], [2, 3], [2, 8], [2, 11], [2, 19], [3, 4], [3, 5], [3, 6], [3, 7], [3, 9], [3, 12], [3, 15], [3, 16], [4, 5], [4, 6], [4, 7], [4, 12], [4, 13], [4, 14], [4, 16], [6, 10], [7, 9], [7, 17], [8, 19], [10, 11], [10, 18], [11, 15], [11, 18]] | undirected | none | {"Substation_2": "0", "Defense_Installation_1": "1", "Strategic_Reserve_Site": "2", "Water_Treatment_Facility": "3", "Nuclear_Facility_Checkpoint": "4", "Oil_Refinery_A": "5", "Tunnel_Entrance_1": "6", "Hospital_Emergency": "7", "Weather_Station_Central": "8", "Fire_Station_Central": "9", "Railway_Hub": "10", "Gas_Dist... | none | node_list |
real_erdos | dominating_set | critical_infrastructure | We're planning emergency shutdown controls for an industrial complex. Facilities are: Chemical_Plant_B, Telecommunications_Hub_A, Pumping_Station_B, City_Hall, Fire_Station_North, Substation_2, Airport_Terminal, Reservoir_Facility, Tunnel_Entrance_1, Strategic_Reserve_Site, Data_Exchange_Point, Emergency_Shelter_1, Hos... | ["Chemical_Plant_B", "Airport_Terminal", "Data_Exchange_Point"] | (0, 14) | [[0, 1], [0, 2], [0, 3], [0, 4], [0, 5], [0, 7], [0, 8], [0, 9], [0, 12], [1, 9], [2, 3], [2, 4], [2, 5], [2, 8], [2, 12], [3, 7], [3, 10], [4, 6], [5, 6], [6, 11], [7, 13], [9, 10], [9, 11], [10, 13]] | undirected | none | {"Chemical_Plant_B": "0", "Telecommunications_Hub_A": "1", "Pumping_Station_B": "2", "City_Hall": "3", "Fire_Station_North": "4", "Substation_2": "5", "Airport_Terminal": "6", "Reservoir_Facility": "7", "Tunnel_Entrance_1": "8", "Strategic_Reserve_Site": "9", "Data_Exchange_Point": "10", "Emergency_Shelter_1": "11", "H... | none | node_list |
real_erdos | dominating_set | critical_infrastructure | We're planning emergency shutdown controls for an industrial complex. Facilities are: Command_Center_North, Pumping_Station_A, Emergency_Shelter_2, Tunnel_Entrance_1, Hospital_Main, Substation_2, Communication_Tower_A, Emergency_Shelter_1, Substation_1, Tunnel_Entrance_2, with infrastructure links: Command_Center_North... | ["Command_Center_North", "Pumping_Station_A", "Hospital_Main", "Substation_1", "Tunnel_Entrance_2"] | (0, 10) | [[0, 2], [0, 6], [1, 3], [1, 5], [1, 6], [1, 7], [2, 7], [2, 9], [3, 5], [3, 9], [5, 6], [6, 7], [7, 9]] | undirected | none | {"Command_Center_North": "0", "Pumping_Station_A": "1", "Emergency_Shelter_2": "2", "Tunnel_Entrance_1": "3", "Hospital_Main": "4", "Substation_2": "5", "Communication_Tower_A": "6", "Emergency_Shelter_1": "7", "Substation_1": "8", "Tunnel_Entrance_2": "9"} | none | node_list |
real_erdos | dominating_set | critical_infrastructure | You're designing a disaster resilience system for urban infrastructure. Critical facilities include: Police_Station_East, Data_Exchange_Point, Hospital_Main, Defense_Installation_1, Fire_Station_Central, Airport_Terminal, Power_Plant_B, Emergency_Shelter_2, Tunnel_Entrance_2, Pumping_Station_B, Fire_Station_North, Bus_... | ["Police_Station_East", "Data_Exchange_Point", "Hospital_Main", "Defense_Installation_1", "Strategic_Reserve_Site"] | (0, 17) | [[0, 5], [0, 12], [1, 4], [1, 5], [1, 8], [1, 13], [1, 16], [2, 5], [2, 6], [2, 9], [2, 11], [2, 15], [3, 4], [3, 6], [3, 7], [3, 8], [3, 9], [3, 10], [3, 12], [4, 6], [4, 7], [4, 9], [4, 11], [4, 12], [4, 14], [4, 15], [5, 7], [5, 12], [5, 14], [6, 11], [6, 14], [7, 11], [7, 16], [8, 9], [8, 10], [9, 11], [9, 14], [9,... | undirected | none | {"Police_Station_East": "0", "Data_Exchange_Point": "1", "Hospital_Main": "2", "Defense_Installation_1": "3", "Fire_Station_Central": "4", "Airport_Terminal": "5", "Power_Plant_B": "6", "Emergency_Shelter_2": "7", "Tunnel_Entrance_2": "8", "Pumping_Station_B": "9", "Fire_Station_North": "10", "Bus_Depot_Central": "11",... | none | node_list |
real_erdos | dominating_set | critical_infrastructure | We're planning emergency shutdown controls for an industrial complex. Facilities are: Strategic_Reserve_Site, Medical_Supply_Center, Bus_Depot_Central, Seismic_Monitor_A, Emergency_Shelter_1, Pumping_Station_A, Communication_Tower_A, Police_Station_East, Bridge_Control_A, Tunnel_Entrance_1, Food_Distribution_Hub, Oil_R... | ["Strategic_Reserve_Site", "Bridge_Control_A", "Oil_Refinery_A", "Dam_Control_Station", "Power_Plant_A", "Emergency_Operations_Center", "Pumping_Station_B"] | (0, 18) | [[0, 1], [0, 2], [0, 3], [0, 4], [0, 5], [0, 6], [0, 7], [0, 9], [0, 10], [0, 14], [1, 7], [2, 3], [2, 5], [2, 6], [2, 11], [3, 4], [3, 15], [5, 8], [5, 12], [5, 13], [6, 8], [6, 9], [6, 12], [6, 16], [7, 17], [9, 10], [9, 11], [9, 13], [9, 14], [9, 15], [9, 17], [13, 16]] | undirected | none | {"Strategic_Reserve_Site": "0", "Medical_Supply_Center": "1", "Bus_Depot_Central": "2", "Seismic_Monitor_A": "3", "Emergency_Shelter_1": "4", "Pumping_Station_A": "5", "Communication_Tower_A": "6", "Police_Station_East": "7", "Bridge_Control_A": "8", "Tunnel_Entrance_1": "9", "Food_Distribution_Hub": "10", "Oil_Refiner... | none | node_list |
real_erdos | dominating_set | critical_infrastructure | A city needs to place security cameras to monitor critical infrastructure. The infrastructure nodes are: Seismic_Monitor_A, Substation_3, Water_Treatment_Facility, Hospital_Main, Emergency_Operations_Center, Data_Exchange_Point, Police_Station_East, Police_Station_West. The physical connections are: Seismic_Monitor_A a... | ["Seismic_Monitor_A", "Water_Treatment_Facility", "Hospital_Main", "Emergency_Operations_Center"] | (0, 8) | [[0, 1], [0, 5], [0, 7], [1, 2], [2, 6], [2, 7], [4, 6], [5, 6], [5, 7], [6, 7]] | undirected | none | {"Seismic_Monitor_A": "0", "Substation_3": "1", "Water_Treatment_Facility": "2", "Hospital_Main": "3", "Emergency_Operations_Center": "4", "Data_Exchange_Point": "5", "Police_Station_East": "6", "Police_Station_West": "7"} | none | node_list |
real_erdos | dominating_set | critical_infrastructure | A city needs to place security cameras to monitor critical infrastructure. The infrastructure nodes are: Emergency_Shelter_1, Data_Exchange_Point, Police_Headquarters, Hospital_Emergency, Dam_Control_Station, Emergency_Operations_Center, Water_Treatment_Facility, Substation_2, Tunnel_Entrance_1, Strategic_Reserve_Site,... | ["Emergency_Shelter_1", "Substation_2", "Strategic_Reserve_Site", "Defense_Installation_1", "Telecommunications_Hub_B", "City_Hall"] | (0, 18) | [[0, 1], [0, 2], [0, 3], [0, 4], [0, 5], [0, 6], [0, 12], [0, 14], [0, 17], [1, 10], [2, 3], [2, 4], [2, 5], [2, 7], [2, 9], [2, 10], [2, 15], [2, 16], [3, 6], [3, 8], [3, 13], [4, 7], [5, 9], [7, 8], [7, 11], [7, 14], [8, 12], [9, 17], [10, 11], [10, 13], [13, 15], [13, 16]] | undirected | none | {"Emergency_Shelter_1": "0", "Data_Exchange_Point": "1", "Police_Headquarters": "2", "Hospital_Emergency": "3", "Dam_Control_Station": "4", "Emergency_Operations_Center": "5", "Water_Treatment_Facility": "6", "Substation_2": "7", "Tunnel_Entrance_1": "8", "Strategic_Reserve_Site": "9", "Defense_Installation_1": "10", "... | none | node_list |
real_erdos | dominating_set | critical_infrastructure | You're designing a disaster resilience system for urban infrastructure. Critical facilities include: Pumping_Station_A, Emergency_Shelter_2, Satellite_Ground_Station, Seismic_Monitor_A, Government_Building_A, Dam_Control_Station, Emergency_Shelter_1, Data_Exchange_Point, Hospital_Main, Police_Headquarters, Pumping_Stat... | ["Pumping_Station_A", "Emergency_Shelter_2", "Satellite_Ground_Station", "Seismic_Monitor_A", "Government_Building_A", "Hospital_Main", "Pumping_Station_B"] | (0, 16) | [[0, 7], [0, 12], [0, 15], [1, 5], [1, 7], [2, 11], [2, 15], [3, 7], [3, 9], [3, 13], [4, 6], [4, 11], [5, 6], [5, 9], [7, 8], [7, 15], [8, 9], [8, 14], [9, 11], [9, 14], [11, 15], [12, 13], [13, 15], [14, 15]] | undirected | none | {"Pumping_Station_A": "0", "Emergency_Shelter_2": "1", "Satellite_Ground_Station": "2", "Seismic_Monitor_A": "3", "Government_Building_A": "4", "Dam_Control_Station": "5", "Emergency_Shelter_1": "6", "Data_Exchange_Point": "7", "Hospital_Main": "8", "Police_Headquarters": "9", "Pumping_Station_B": "10", "Reservoir_Faci... | none | node_list |
real_erdos | dominating_set | critical_infrastructure | A city needs to place security cameras to monitor critical infrastructure. The infrastructure nodes are: Data_Exchange_Point, Command_Center_North, Port_Authority, Strategic_Reserve_Site, Weather_Station_Central, Seismic_Monitor_A, Satellite_Ground_Station, Pumping_Station_B, Telecommunications_Hub_A, Reservoir_Facilit... | ["Data_Exchange_Point", "Command_Center_North", "Port_Authority", "Pumping_Station_B", "Reservoir_Facility"] | (0, 14) | [[0, 3], [0, 4], [1, 3], [1, 5], [1, 6], [1, 10], [1, 11], [1, 12], [2, 10], [2, 13], [3, 4], [3, 6], [3, 13], [4, 7], [5, 8], [5, 9], [5, 10], [5, 11], [5, 12], [6, 8], [6, 9], [7, 8], [7, 10], [7, 11], [7, 13], [9, 13], [11, 13]] | undirected | none | {"Data_Exchange_Point": "0", "Command_Center_North": "1", "Port_Authority": "2", "Strategic_Reserve_Site": "3", "Weather_Station_Central": "4", "Seismic_Monitor_A": "5", "Satellite_Ground_Station": "6", "Pumping_Station_B": "7", "Telecommunications_Hub_A": "8", "Reservoir_Facility": "9", "Substation_2": "10", "Bridge_C... | none | node_list |
real_erdos | dominating_set | data_center_power | We're deploying energy monitors in a server farm. Server locations: Blade_Server_2, UPS_Zone_1, Load_Balancer_B, Blade_Server_1, Network_Switch_1, Compute_Unit_Gamma, Cluster_Node_1, VM_Host_B, Redundant_Unit_A, Rack_B2, Edge_Server_2, VM_Host_A, Rack_C1, PDU_North, Server_Node_2, Storage_Array_B, Blade_Server_3, Serve... | ["Blade_Server_2", "Compute_Unit_Gamma", "Cluster_Node_1", "Storage_Array_B"] | (0, 20) | [[0, 1], [0, 2], [0, 3], [0, 4], [0, 8], [0, 12], [0, 14], [0, 19], [1, 6], [2, 4], [2, 5], [2, 7], [2, 16], [3, 4], [3, 5], [3, 6], [3, 9], [3, 10], [3, 13], [4, 5], [4, 6], [4, 7], [4, 18], [5, 7], [5, 8], [5, 11], [5, 12], [5, 13], [5, 18], [6, 8], [6, 9], [6, 10], [6, 16], [7, 9], [7, 14], [7, 15], [8, 10], [8, 11]... | undirected | none | {"Blade_Server_2": "0", "UPS_Zone_1": "1", "Load_Balancer_B": "2", "Blade_Server_1": "3", "Network_Switch_1": "4", "Compute_Unit_Gamma": "5", "Cluster_Node_1": "6", "VM_Host_B": "7", "Redundant_Unit_A": "8", "Rack_B2": "9", "Edge_Server_2": "10", "VM_Host_A": "11", "Rack_C1": "12", "PDU_North": "13", "Server_Node_2": "... | none | node_list |
real_erdos | dominating_set | data_center_power | We're deploying energy monitors in a server farm. Server locations: Generator_Connection_B, Cooling_Zone_1, Cabinet_Row_A, Server_Node_4, Server_Node_1, VM_Host_B, Edge_Server_2, Redundant_Unit_B, Rack_A1, Core_Server_A, Rack_C2, with connections: Generator_Connection_B is connected to Server_Node_4 via power distribut... | ["Generator_Connection_B", "Cooling_Zone_1", "Cabinet_Row_A", "VM_Host_B"] | (0, 11) | [[0, 3], [0, 4], [0, 8], [0, 9], [0, 10], [1, 3], [1, 7], [2, 10], [3, 5], [3, 8], [3, 9], [4, 5], [4, 7], [4, 8], [5, 6], [5, 10], [7, 8]] | undirected | none | {"Generator_Connection_B": "0", "Cooling_Zone_1": "1", "Cabinet_Row_A": "2", "Server_Node_4": "3", "Server_Node_1": "4", "VM_Host_B": "5", "Edge_Server_2": "6", "Redundant_Unit_B": "7", "Rack_A1": "8", "Core_Server_A": "9", "Rack_C2": "10"} | none | node_list |
real_erdos | dominating_set | data_center_power | You're optimizing power management for a distributed computing facility. The compute nodes are: Core_Server_B, Generator_Connection_B, Rack_A1, Storage_Array_A, Cabinet_Row_B, Cluster_Node_2, UPS_Zone_1, Storage_Array_D, Rack_C2, connected as: Core_Server_B is connected to Storage_Array_D via power distribution. Genera... | ["Core_Server_B", "Generator_Connection_B", "Rack_A1", "Cabinet_Row_B"] | (0, 9) | [[0, 7], [1, 3], [1, 7], [1, 8], [2, 6], [2, 7], [2, 8], [3, 4], [3, 7], [3, 8], [4, 5], [5, 6], [5, 8], [6, 8], [7, 8]] | undirected | none | {"Core_Server_B": "0", "Generator_Connection_B": "1", "Rack_A1": "2", "Storage_Array_A": "3", "Cabinet_Row_B": "4", "Cluster_Node_2": "5", "UPS_Zone_1": "6", "Storage_Array_D": "7", "Rack_C2": "8"} | none | node_list |
real_erdos | dominating_set | data_center_power | A data center has multiple server racks that need power monitoring. The racks are: Server_Node_3, Blade_Server_4, VM_Host_B, Storage_Array_A, Server_Node_1, Power_Distribution_Unit_2, Compute_Unit_Beta, Edge_Server_2, Cooling_Zone_2, Compute_Unit_Alpha, Cooling_Zone_1, Cluster_Node_1, UPS_Zone_1, VM_Host_A, UPS_Zone_2,... | ["Server_Node_3", "Blade_Server_4", "Power_Distribution_Unit_2", "Edge_Server_2", "Cooling_Zone_2", "Cluster_Node_1", "UPS_Zone_2", "Core_Server_A"] | (0, 20) | [[0, 3], [0, 4], [0, 6], [0, 9], [0, 19], [1, 2], [1, 4], [1, 6], [1, 9], [1, 18], [2, 3], [2, 4], [2, 5], [2, 6], [2, 13], [3, 6], [3, 10], [3, 14], [4, 8], [4, 14], [4, 18], [5, 13], [5, 15], [5, 19], [7, 9], [7, 10], [7, 12], [7, 18], [8, 10], [8, 18], [9, 16], [10, 14], [10, 15], [11, 17], [12, 16], [12, 18], [13, ... | undirected | none | {"Server_Node_3": "0", "Blade_Server_4": "1", "VM_Host_B": "2", "Storage_Array_A": "3", "Server_Node_1": "4", "Power_Distribution_Unit_2": "5", "Compute_Unit_Beta": "6", "Edge_Server_2": "7", "Cooling_Zone_2": "8", "Compute_Unit_Alpha": "9", "Cooling_Zone_1": "10", "Cluster_Node_1": "11", "UPS_Zone_1": "12", "VM_Host_A... | none | node_list |
real_erdos | dominating_set | data_center_power | A cloud infrastructure requires backup power units. Servers are arranged as: Edge_Server_1, Cluster_Node_1, Server_Node_1, Backup_Node_2, Storage_Array_A, Rack_A2, Compute_Unit_Gamma, Cabinet_Row_A, UPS_Zone_2, Rack_B2, Load_Balancer_A, Compute_Unit_Alpha, Cooling_Zone_1, Rack_B1, with network topology: Edge_Server_1 i... | ["Edge_Server_1", "Cluster_Node_1", "Server_Node_1", "Compute_Unit_Gamma", "Cabinet_Row_A"] | (0, 14) | [[0, 3], [0, 4], [0, 10], [0, 11], [0, 13], [1, 5], [1, 10], [1, 12], [2, 3], [2, 9], [2, 12], [3, 5], [3, 7], [3, 8], [3, 11], [4, 6], [4, 8], [4, 9], [5, 10], [6, 8], [6, 10], [7, 9], [9, 12], [9, 13], [10, 11], [12, 13]] | undirected | none | {"Edge_Server_1": "0", "Cluster_Node_1": "1", "Server_Node_1": "2", "Backup_Node_2": "3", "Storage_Array_A": "4", "Rack_A2": "5", "Compute_Unit_Gamma": "6", "Cabinet_Row_A": "7", "UPS_Zone_2": "8", "Rack_B2": "9", "Load_Balancer_A": "10", "Compute_Unit_Alpha": "11", "Cooling_Zone_1": "12", "Rack_B1": "13"} | none | node_list |
real_erdos | dominating_set | data_center_power | We're deploying energy monitors in a server farm. Server locations: Storage_Array_C, Rack_B2, Storage_Array_D, Blade_Server_1, Rack_C2, Cluster_Node_2, Server_Node_1, Redundant_Unit_B, Cluster_Node_1, Cooling_Zone_1, UPS_Zone_2, Backup_Node_1, PDU_South, VM_Host_A, Core_Server_B, Blade_Server_3, Load_Balancer_A, Server... | ["Storage_Array_C", "UPS_Zone_2", "Blade_Server_3", "Load_Balancer_A", "Server_Node_4", "Edge_Server_2"] | (0, 20) | [[0, 1], [0, 2], [0, 3], [0, 4], [0, 5], [0, 6], [0, 7], [0, 8], [0, 9], [0, 12], [0, 13], [0, 14], [0, 19], [1, 3], [1, 4], [1, 7], [1, 9], [1, 10], [1, 15], [1, 17], [1, 18], [2, 5], [2, 13], [2, 14], [4, 8], [5, 6], [6, 16], [7, 10], [8, 11], [10, 11], [11, 12], [11, 18], [11, 19], [12, 15], [12, 17], [13, 16]] | undirected | none | {"Storage_Array_C": "0", "Rack_B2": "1", "Storage_Array_D": "2", "Blade_Server_1": "3", "Rack_C2": "4", "Cluster_Node_2": "5", "Server_Node_1": "6", "Redundant_Unit_B": "7", "Cluster_Node_1": "8", "Cooling_Zone_1": "9", "UPS_Zone_2": "10", "Backup_Node_1": "11", "PDU_South": "12", "VM_Host_A": "13", "Core_Server_B": "1... | none | node_list |
real_erdos | dominating_set | data_center_power | A data center has multiple server racks that need power monitoring. The racks are: PDU_North, Server_Node_4, Blade_Server_4, Rack_B1, Blade_Server_2, Power_Distribution_Unit_1, Redundant_Unit_B, Server_Node_3, Edge_Server_2, Rack_A2, PDU_South. Power distribution follows this network: PDU_North shares power infrastruct... | ["PDU_North", "Server_Node_4", "Blade_Server_4", "Redundant_Unit_B"] | (0, 11) | [[0, 4], [0, 5], [0, 9], [0, 10], [1, 3], [1, 8], [1, 10], [2, 7], [2, 9], [2, 10], [3, 4], [3, 8], [3, 10], [4, 5], [4, 9], [4, 10], [5, 10], [6, 7], [7, 10]] | undirected | none | {"PDU_North": "0", "Server_Node_4": "1", "Blade_Server_4": "2", "Rack_B1": "3", "Blade_Server_2": "4", "Power_Distribution_Unit_1": "5", "Redundant_Unit_B": "6", "Server_Node_3": "7", "Edge_Server_2": "8", "Rack_A2": "9", "PDU_South": "10"} | none | node_list |
real_erdos | dominating_set | data_center_power | You're optimizing power management for a distributed computing facility. The compute nodes are: VM_Host_A, Load_Balancer_A, Rack_B1, Cabinet_Row_A, Power_Distribution_Unit_1, Cooling_Zone_1, Server_Node_2, PDU_North, Blade_Server_4, Storage_Array_B, connected as: There is a power connection from VM_Host_A to Power_Dist... | ["VM_Host_A", "Load_Balancer_A", "Rack_B1", "Cabinet_Row_A", "PDU_North", "Blade_Server_4"] | (0, 10) | [[0, 4], [1, 5], [1, 9], [2, 5], [2, 6], [3, 4], [3, 5], [6, 7], [6, 9], [7, 9]] | undirected | none | {"VM_Host_A": "0", "Load_Balancer_A": "1", "Rack_B1": "2", "Cabinet_Row_A": "3", "Power_Distribution_Unit_1": "4", "Cooling_Zone_1": "5", "Server_Node_2": "6", "PDU_North": "7", "Blade_Server_4": "8", "Storage_Array_B": "9"} | none | node_list |
real_erdos | dominating_set | data_center_power | A data center has multiple server racks that need power monitoring. The racks are: Power_Distribution_Unit_1, Load_Balancer_A, Compute_Unit_Gamma, Redundant_Unit_A, Storage_Array_B, Core_Server_B, Backup_Node_1, UPS_Zone_2, Cooling_Zone_1, Compute_Unit_Delta, Cluster_Node_1, Blade_Server_2, Cabinet_Row_B, Rack_C2, VM_H... | ["Power_Distribution_Unit_1", "Load_Balancer_A", "Compute_Unit_Gamma", "Redundant_Unit_A", "Core_Server_B", "Backup_Node_1", "VM_Host_B", "Edge_Server_1"] | (0, 19) | [[0, 4], [0, 9], [0, 10], [0, 11], [0, 13], [0, 17], [0, 18], [1, 8], [1, 9], [1, 10], [1, 12], [2, 10], [2, 11], [2, 17], [2, 18], [3, 7], [3, 9], [3, 12], [3, 16], [4, 12], [4, 13], [4, 14], [4, 16], [5, 11], [5, 18], [6, 12], [7, 11], [7, 16], [8, 11], [8, 13], [9, 10], [9, 13], [10, 11], [10, 12], [10, 13], [10, 17... | undirected | none | {"Power_Distribution_Unit_1": "0", "Load_Balancer_A": "1", "Compute_Unit_Gamma": "2", "Redundant_Unit_A": "3", "Storage_Array_B": "4", "Core_Server_B": "5", "Backup_Node_1": "6", "UPS_Zone_2": "7", "Cooling_Zone_1": "8", "Compute_Unit_Delta": "9", "Cluster_Node_1": "10", "Blade_Server_2": "11", "Cabinet_Row_B": "12", "... | none | node_list |
real_erdos | dominating_set | data_center_power | You're optimizing power management for a distributed computing facility. The compute nodes are: Server_Node_2, Cluster_Node_1, Server_Node_1, Power_Distribution_Unit_2, PDU_North, Redundant_Unit_B, Rack_C1, Load_Balancer_A, Edge_Server_1, Server_Node_3, Backup_Node_2, Blade_Server_2, VM_Host_B, Rack_B2, Cluster_Node_2,... | ["Server_Node_2", "Power_Distribution_Unit_2", "PDU_North", "Rack_C1", "Blade_Server_2", "Cluster_Node_2"] | (0, 20) | [[0, 1], [0, 2], [0, 5], [0, 7], [0, 9], [0, 10], [0, 16], [0, 18], [1, 6], [1, 11], [1, 12], [1, 13], [2, 5], [2, 8], [2, 10], [2, 13], [2, 15], [2, 18], [3, 8], [3, 10], [3, 12], [3, 19], [4, 8], [4, 9], [4, 12], [4, 15], [4, 17], [4, 19], [5, 7], [5, 17], [6, 12], [6, 16], [6, 17], [6, 19], [7, 10], [7, 15], [7, 17]... | undirected | none | {"Server_Node_2": "0", "Cluster_Node_1": "1", "Server_Node_1": "2", "Power_Distribution_Unit_2": "3", "PDU_North": "4", "Redundant_Unit_B": "5", "Rack_C1": "6", "Load_Balancer_A": "7", "Edge_Server_1": "8", "Server_Node_3": "9", "Backup_Node_2": "10", "Blade_Server_2": "11", "VM_Host_B": "12", "Rack_B2": "13", "Cluster... | none | node_list |
real_erdos | dominating_set | data_center_power | You're optimizing power management for a distributed computing facility. The compute nodes are: Storage_Array_B, Cluster_Node_1, Redundant_Unit_B, Backup_Node_1, Compute_Unit_Alpha, VM_Host_B, Storage_Array_D, Cooling_Zone_1, Storage_Array_A, Power_Distribution_Unit_1, Server_Node_3, Compute_Unit_Gamma, Compute_Unit_Be... | ["Storage_Array_B", "Storage_Array_D", "Storage_Array_A", "Power_Distribution_Unit_1", "Compute_Unit_Gamma", "Server_Node_1", "Rack_B1"] | (0, 20) | [[0, 1], [0, 2], [0, 3], [0, 4], [0, 5], [0, 7], [0, 10], [0, 13], [0, 17], [1, 4], [1, 6], [1, 11], [1, 13], [1, 15], [1, 19], [2, 3], [2, 5], [2, 6], [2, 7], [2, 8], [2, 12], [3, 11], [3, 18], [4, 8], [4, 9], [4, 14], [6, 14], [7, 9], [7, 16], [8, 10], [9, 12], [9, 15], [9, 17], [11, 16], [15, 18], [16, 19]] | undirected | none | {"Storage_Array_B": "0", "Cluster_Node_1": "1", "Redundant_Unit_B": "2", "Backup_Node_1": "3", "Compute_Unit_Alpha": "4", "VM_Host_B": "5", "Storage_Array_D": "6", "Cooling_Zone_1": "7", "Storage_Array_A": "8", "Power_Distribution_Unit_1": "9", "Server_Node_3": "10", "Compute_Unit_Gamma": "11", "Compute_Unit_Beta": "12... | none | node_list |
real_erdos | dominating_set | data_center_power | We're deploying energy monitors in a server farm. Server locations: Load_Balancer_A, Core_Server_B, Rack_B1, Network_Switch_1, Server_Node_3, Redundant_Unit_A, Compute_Unit_Delta, Power_Distribution_Unit_2, Blade_Server_2, Backup_Node_2, Compute_Unit_Gamma, Storage_Array_B, Edge_Server_2, Redundant_Unit_B, Blade_Server... | ["Load_Balancer_A", "Core_Server_B", "Rack_B1", "Power_Distribution_Unit_2", "Edge_Server_2", "Redundant_Unit_B", "Blade_Server_4"] | (0, 18) | [[0, 3], [0, 4], [0, 5], [0, 6], [0, 9], [0, 10], [1, 4], [1, 5], [1, 6], [1, 8], [1, 11], [2, 10], [2, 16], [3, 4], [3, 5], [3, 8], [3, 9], [3, 11], [4, 10], [4, 11], [5, 6], [5, 8], [5, 11], [6, 9], [6, 10], [6, 13], [6, 16], [7, 8], [7, 11], [8, 11], [8, 14], [9, 17], [11, 14], [12, 15], [12, 17], [14, 16], [16, 17]... | undirected | none | {"Load_Balancer_A": "0", "Core_Server_B": "1", "Rack_B1": "2", "Network_Switch_1": "3", "Server_Node_3": "4", "Redundant_Unit_A": "5", "Compute_Unit_Delta": "6", "Power_Distribution_Unit_2": "7", "Blade_Server_2": "8", "Backup_Node_2": "9", "Compute_Unit_Gamma": "10", "Storage_Array_B": "11", "Edge_Server_2": "12", "Re... | none | node_list |
real_erdos | dominating_set | data_center_power | You're optimizing power management for a distributed computing facility. The compute nodes are: Edge_Server_1, Server_Node_2, Rack_B1, Network_Switch_1, Blade_Server_3, Storage_Array_B, Blade_Server_1, Compute_Unit_Alpha, Core_Server_A, Edge_Server_2, Cooling_Zone_1, Server_Node_4, Blade_Server_4, Power_Distribution_Un... | ["Edge_Server_1", "Network_Switch_1", "Storage_Array_B"] | (0, 15) | [[0, 1], [0, 2], [0, 4], [0, 7], [0, 8], [0, 10], [0, 11], [0, 13], [1, 5], [1, 6], [1, 8], [1, 11], [2, 5], [2, 6], [2, 7], [3, 6], [3, 11], [3, 12], [4, 9], [4, 13], [5, 7], [5, 9], [5, 10], [5, 11], [5, 14], [6, 9], [6, 14], [8, 9], [8, 14], [9, 11], [9, 13], [10, 13], [11, 14]] | undirected | none | {"Edge_Server_1": "0", "Server_Node_2": "1", "Rack_B1": "2", "Network_Switch_1": "3", "Blade_Server_3": "4", "Storage_Array_B": "5", "Blade_Server_1": "6", "Compute_Unit_Alpha": "7", "Core_Server_A": "8", "Edge_Server_2": "9", "Cooling_Zone_1": "10", "Server_Node_4": "11", "Blade_Server_4": "12", "Power_Distribution_Un... | none | node_list |
real_erdos | dominating_set | data_center_power | You're optimizing power management for a distributed computing facility. The compute nodes are: Compute_Unit_Delta, Rack_A2, PDU_South, Storage_Array_C, Rack_A1, UPS_Zone_1, Cluster_Node_2, Redundant_Unit_B, Cluster_Node_1, Cooling_Zone_1, Network_Switch_2, VM_Host_B, Backup_Node_1, connected as: Compute_Unit_Delta and... | ["Compute_Unit_Delta", "Storage_Array_C", "Rack_A1", "UPS_Zone_1", "Cluster_Node_2", "Redundant_Unit_B", "Cluster_Node_1", "Backup_Node_1"] | (0, 13) | [[0, 1], [0, 2], [0, 10], [1, 2], [1, 5], [2, 8], [2, 12], [5, 11], [6, 9], [7, 9], [7, 10], [8, 9], [8, 10], [11, 12]] | undirected | none | {"Compute_Unit_Delta": "0", "Rack_A2": "1", "PDU_South": "2", "Storage_Array_C": "3", "Rack_A1": "4", "UPS_Zone_1": "5", "Cluster_Node_2": "6", "Redundant_Unit_B": "7", "Cluster_Node_1": "8", "Cooling_Zone_1": "9", "Network_Switch_2": "10", "VM_Host_B": "11", "Backup_Node_1": "12"} | none | node_list |
real_erdos | dominating_set | data_center_power | We're deploying energy monitors in a server farm. Server locations: Edge_Server_2, Cooling_Zone_2, Compute_Unit_Delta, Cluster_Node_1, Generator_Connection_B, Blade_Server_3, Network_Switch_1, Rack_A2, Blade_Server_1, UPS_Zone_2, Core_Server_B, Compute_Unit_Alpha, Backup_Node_1, Storage_Array_C, Blade_Server_2, Power_D... | ["Edge_Server_2", "Cooling_Zone_2", "Cluster_Node_1", "Generator_Connection_B", "Network_Switch_2", "Power_Distribution_Unit_1"] | (0, 20) | [[0, 2], [0, 5], [0, 8], [0, 9], [1, 2], [1, 14], [2, 3], [2, 7], [2, 12], [2, 13], [2, 18], [3, 5], [3, 8], [3, 12], [3, 18], [4, 5], [4, 6], [4, 7], [4, 10], [4, 11], [4, 12], [4, 13], [4, 15], [4, 17], [5, 7], [5, 8], [5, 11], [5, 19], [6, 8], [6, 11], [6, 12], [7, 11], [7, 16], [7, 19], [8, 10], [8, 15], [9, 12], [... | undirected | none | {"Edge_Server_2": "0", "Cooling_Zone_2": "1", "Compute_Unit_Delta": "2", "Cluster_Node_1": "3", "Generator_Connection_B": "4", "Blade_Server_3": "5", "Network_Switch_1": "6", "Rack_A2": "7", "Blade_Server_1": "8", "UPS_Zone_2": "9", "Core_Server_B": "10", "Compute_Unit_Alpha": "11", "Backup_Node_1": "12", "Storage_Arra... | none | node_list |
real_erdos | dominating_set | data_center_power | We're deploying energy monitors in a server farm. Server locations: Core_Server_A, Compute_Unit_Alpha, Edge_Server_1, PDU_South, Redundant_Unit_A, Cluster_Node_1, Blade_Server_3, Server_Node_4, PDU_North, Storage_Array_D, with connections: Core_Server_A is connected to Edge_Server_1 via power distribution. Core_Server_... | ["Core_Server_A", "Compute_Unit_Alpha", "PDU_South", "Redundant_Unit_A", "Blade_Server_3"] | (0, 10) | [[0, 2], [0, 5], [0, 9], [1, 5], [1, 8], [2, 3], [2, 7], [2, 8], [3, 9], [4, 7], [5, 7]] | undirected | none | {"Core_Server_A": "0", "Compute_Unit_Alpha": "1", "Edge_Server_1": "2", "PDU_South": "3", "Redundant_Unit_A": "4", "Cluster_Node_1": "5", "Blade_Server_3": "6", "Server_Node_4": "7", "PDU_North": "8", "Storage_Array_D": "9"} | none | node_list |
real_erdos | dominating_set | data_center_power | A data center has multiple server racks that need power monitoring. The racks are: Edge_Server_1, Power_Distribution_Unit_2, Storage_Array_A, VM_Host_A, Storage_Array_D, Compute_Unit_Alpha, Rack_A2, Backup_Node_2, Server_Node_4, Compute_Unit_Delta, Blade_Server_4, Compute_Unit_Gamma, Redundant_Unit_A, Rack_B2, Server_N... | ["Edge_Server_1", "Storage_Array_A", "VM_Host_A", "Storage_Array_D", "Server_Node_2"] | (0, 15) | [[0, 1], [0, 5], [0, 6], [0, 7], [0, 12], [1, 5], [1, 9], [1, 11], [1, 12], [1, 13], [2, 7], [2, 8], [2, 11], [2, 12], [2, 13], [3, 7], [3, 9], [3, 10], [3, 13], [4, 13], [5, 7], [5, 8], [5, 11], [5, 14], [6, 7], [6, 8], [6, 9], [6, 10], [6, 13], [6, 14], [7, 9], [7, 13], [8, 10], [8, 11], [9, 10], [9, 12], [10, 12], [... | undirected | none | {"Edge_Server_1": "0", "Power_Distribution_Unit_2": "1", "Storage_Array_A": "2", "VM_Host_A": "3", "Storage_Array_D": "4", "Compute_Unit_Alpha": "5", "Rack_A2": "6", "Backup_Node_2": "7", "Server_Node_4": "8", "Compute_Unit_Delta": "9", "Blade_Server_4": "10", "Compute_Unit_Gamma": "11", "Redundant_Unit_A": "12", "Rack... | none | node_list |
real_erdos | dominating_set | data_center_power | You're optimizing power management for a distributed computing facility. The compute nodes are: PDU_South, Compute_Unit_Gamma, UPS_Zone_1, Network_Switch_2, Redundant_Unit_A, Cooling_Zone_2, Rack_B1, Power_Distribution_Unit_1, Server_Node_1, Redundant_Unit_B, Core_Server_A, connected as: PDU_South has a direct power li... | ["PDU_South", "Compute_Unit_Gamma", "UPS_Zone_1", "Cooling_Zone_2", "Redundant_Unit_B"] | (0, 11) | [[0, 3], [0, 6], [2, 4], [2, 6], [2, 7], [3, 4], [3, 5], [3, 6], [3, 9], [4, 5], [4, 6], [4, 7], [4, 10], [5, 8], [5, 10], [7, 9]] | undirected | none | {"PDU_South": "0", "Compute_Unit_Gamma": "1", "UPS_Zone_1": "2", "Network_Switch_2": "3", "Redundant_Unit_A": "4", "Cooling_Zone_2": "5", "Rack_B1": "6", "Power_Distribution_Unit_1": "7", "Server_Node_1": "8", "Redundant_Unit_B": "9", "Core_Server_A": "10"} | none | node_list |
real_erdos | dominating_set | data_center_power | You're optimizing power management for a distributed computing facility. The compute nodes are: Compute_Unit_Gamma, Compute_Unit_Delta, Rack_B1, Power_Distribution_Unit_1, Cabinet_Row_A, Server_Node_4, Cooling_Zone_1, Rack_B2, VM_Host_B, Cluster_Node_2, Backup_Node_1, Storage_Array_C, Storage_Array_A, Core_Server_B, Se... | ["Compute_Unit_Gamma", "Compute_Unit_Delta", "Rack_B1", "Server_Node_4", "Rack_B2", "Storage_Array_C", "Core_Server_B", "Network_Switch_2"] | (0, 20) | [[0, 18], [0, 19], [1, 3], [1, 4], [1, 6], [1, 8], [1, 19], [3, 5], [3, 6], [3, 13], [3, 17], [4, 6], [4, 8], [4, 9], [4, 10], [4, 12], [4, 17], [5, 10], [5, 14], [5, 19], [6, 9], [6, 12], [6, 15], [6, 17], [6, 18], [7, 9], [9, 12], [9, 16], [9, 17], [9, 18], [10, 15], [10, 19], [11, 12], [11, 15], [11, 16], [11, 18], ... | undirected | none | {"Compute_Unit_Gamma": "0", "Compute_Unit_Delta": "1", "Rack_B1": "2", "Power_Distribution_Unit_1": "3", "Cabinet_Row_A": "4", "Server_Node_4": "5", "Cooling_Zone_1": "6", "Rack_B2": "7", "VM_Host_B": "8", "Cluster_Node_2": "9", "Backup_Node_1": "10", "Storage_Array_C": "11", "Storage_Array_A": "12", "Core_Server_B": "... | none | node_list |
real_erdos | dominating_set | data_center_power | You're optimizing power management for a distributed computing facility. The compute nodes are: Rack_A1, VM_Host_A, Cluster_Node_1, Blade_Server_4, UPS_Zone_1, Rack_B1, Load_Balancer_B, Cabinet_Row_B, Cabinet_Row_A, Rack_C1, Rack_A2, Core_Server_A, Blade_Server_2, PDU_South, Network_Switch_2, Cluster_Node_2, Compute_Un... | ["Rack_A1", "Cabinet_Row_A", "Rack_C1", "Rack_A2", "PDU_South", "Cluster_Node_2", "Storage_Array_B"] | (0, 20) | [[0, 1], [0, 2], [0, 3], [0, 4], [0, 5], [0, 6], [0, 7], [0, 14], [2, 4], [2, 10], [2, 12], [2, 18], [3, 4], [3, 5], [3, 6], [3, 8], [4, 5], [4, 7], [4, 8], [4, 9], [4, 11], [4, 15], [5, 6], [5, 7], [6, 9], [6, 10], [6, 13], [6, 15], [6, 16], [7, 8], [7, 9], [7, 10], [7, 13], [7, 18], [8, 11], [8, 12], [8, 17], [10, 11... | undirected | none | {"Rack_A1": "0", "VM_Host_A": "1", "Cluster_Node_1": "2", "Blade_Server_4": "3", "UPS_Zone_1": "4", "Rack_B1": "5", "Load_Balancer_B": "6", "Cabinet_Row_B": "7", "Cabinet_Row_A": "8", "Rack_C1": "9", "Rack_A2": "10", "Core_Server_A": "11", "Blade_Server_2": "12", "PDU_South": "13", "Network_Switch_2": "14", "Cluster_No... | none | node_list |
real_erdos | dominating_set | sensor_network_deployment | You're deploying environmental sensors across a monitoring area. Potential sensor locations are: Sample_Point_1, Monitoring_Point_4, Air_Quality_Point_1, Temperature_Probe_1, Sensor_Location_C, Grid_Cell_B1, Sensor_Location_A, Wildlife_Camera_2, Detector_Site_B, Motion_Detector_B, Camera_Position_3, Zone_Alpha, Humidit... | ["Sample_Point_1", "Monitoring_Point_4", "Air_Quality_Point_1", "Temperature_Probe_1", "Sensor_Location_A", "Water_Sensor_2"] | (0, 17) | [[0, 4], [0, 5], [0, 7], [0, 11], [0, 13], [0, 15], [1, 5], [1, 7], [1, 13], [1, 14], [2, 4], [2, 5], [2, 8], [2, 12], [2, 14], [3, 10], [4, 10], [4, 12], [4, 16], [5, 6], [5, 12], [5, 14], [6, 7], [6, 8], [6, 9], [6, 13], [6, 14], [7, 8], [7, 11], [7, 15], [7, 16], [8, 14], [8, 16], [9, 10], [9, 12], [9, 15], [9, 16],... | undirected | none | {"Sample_Point_1": "0", "Monitoring_Point_4": "1", "Air_Quality_Point_1": "2", "Temperature_Probe_1": "3", "Sensor_Location_C": "4", "Grid_Cell_B1": "5", "Sensor_Location_A": "6", "Wildlife_Camera_2": "7", "Detector_Site_B": "8", "Motion_Detector_B": "9", "Camera_Position_3": "10", "Zone_Alpha": "11", "Humidity_Sensor_... | none | node_list |
real_erdos | dominating_set | sensor_network_deployment | You're deploying environmental sensors across a monitoring area. Potential sensor locations are: Sensor_Location_C, Sample_Point_4, Monitoring_Point_2, Grid_Cell_A1, Checkpoint_North, Zone_Epsilon, Zone_Alpha, Camera_Position_2, Water_Sensor_1, Temperature_Probe_2, Zone_Delta, Camera_Position_3, Checkpoint_West, Zone_B... | ["Sensor_Location_C", "Camera_Position_2", "Water_Sensor_1", "Camera_Position_3", "Temperature_Probe_1"] | (0, 18) | [[0, 1], [0, 2], [0, 3], [0, 4], [0, 5], [0, 6], [0, 9], [0, 10], [0, 12], [0, 13], [0, 15], [1, 3], [1, 8], [2, 5], [3, 4], [3, 6], [3, 7], [3, 9], [4, 10], [4, 11], [4, 15], [5, 7], [5, 8], [8, 12], [8, 14], [8, 17], [9, 11], [9, 13], [10, 17], [13, 14], [14, 16], [15, 16]] | undirected | none | {"Sensor_Location_C": "0", "Sample_Point_4": "1", "Monitoring_Point_2": "2", "Grid_Cell_A1": "3", "Checkpoint_North": "4", "Zone_Epsilon": "5", "Zone_Alpha": "6", "Camera_Position_2": "7", "Water_Sensor_1": "8", "Temperature_Probe_2": "9", "Zone_Delta": "10", "Camera_Position_3": "11", "Checkpoint_West": "12", "Zone_Be... | none | node_list |
real_erdos | dominating_set | sensor_network_deployment | A smart city project requires air quality sensors. Installation points: Sensor_Location_C, Checkpoint_North, Observation_Post_2, Monitoring_Point_1, Checkpoint_West, Wildlife_Camera_1, Air_Quality_Point_1, Monitoring_Point_2, Sensor_Location_B, Temperature_Probe_1, Motion_Detector_B, Water_Sensor_2, Zone_Alpha, Humidit... | ["Sensor_Location_C", "Checkpoint_North", "Monitoring_Point_1", "Wildlife_Camera_1", "Sensor_Location_B", "Humidity_Sensor_B"] | (0, 15) | [[1, 2], [1, 6], [1, 7], [1, 9], [1, 14], [2, 5], [2, 7], [2, 12], [3, 4], [3, 7], [3, 9], [3, 11], [4, 7], [5, 6], [5, 10], [6, 7], [6, 9], [6, 13], [7, 8], [8, 10], [8, 12], [8, 14], [9, 14], [10, 13], [11, 12]] | undirected | none | {"Sensor_Location_C": "0", "Checkpoint_North": "1", "Observation_Post_2": "2", "Monitoring_Point_1": "3", "Checkpoint_West": "4", "Wildlife_Camera_1": "5", "Air_Quality_Point_1": "6", "Monitoring_Point_2": "7", "Sensor_Location_B": "8", "Temperature_Probe_1": "9", "Motion_Detector_B": "10", "Water_Sensor_2": "11", "Zon... | none | node_list |
real_erdos | dominating_set | sensor_network_deployment | A smart city project requires air quality sensors. Installation points: Sample_Point_3, Motion_Detector_A, Humidity_Sensor_B, Environmental_Station_B, Detector_Site_C, Camera_Position_2, Monitoring_Point_3, Air_Quality_Point_1, Wildlife_Camera_2, Water_Sensor_1, Camera_Position_4, Zone_Beta, Sensor_Location_D, Water_Se... | ["Sample_Point_3", "Motion_Detector_A", "Camera_Position_2", "Monitoring_Point_3", "Air_Quality_Point_1", "Camera_Position_4"] | (0, 16) | [[0, 2], [0, 3], [0, 8], [0, 9], [0, 12], [0, 14], [1, 4], [1, 11], [2, 4], [2, 8], [2, 13], [3, 7], [3, 8], [3, 9], [3, 10], [4, 5], [4, 8], [5, 11], [5, 13], [6, 11], [6, 12], [7, 9], [7, 14], [7, 15], [8, 9], [8, 13], [9, 13], [10, 11], [11, 12], [11, 13], [12, 14], [12, 15], [13, 15]] | undirected | none | {"Sample_Point_3": "0", "Motion_Detector_A": "1", "Humidity_Sensor_B": "2", "Environmental_Station_B": "3", "Detector_Site_C": "4", "Camera_Position_2": "5", "Monitoring_Point_3": "6", "Air_Quality_Point_1": "7", "Wildlife_Camera_2": "8", "Water_Sensor_1": "9", "Camera_Position_4": "10", "Zone_Beta": "11", "Sensor_Loca... | none | node_list |
real_erdos | dominating_set | sensor_network_deployment | We're setting up a wildlife monitoring network in a nature reserve. Monitoring zones are: Monitoring_Point_4, Temperature_Probe_1, Observation_Post_2, Humidity_Sensor_B, Grid_Cell_A2, Detector_Site_D, Soil_Monitor_B, Sample_Point_1, Sensor_Location_C, Temperature_Probe_2, Sample_Point_4, Zone_Alpha, Zone_Beta, Soil_Mon... | ["Monitoring_Point_4", "Soil_Monitor_B", "Sample_Point_4", "Zone_Alpha", "Soil_Monitor_A", "Monitoring_Point_3"] | (0, 15) | [[0, 1], [0, 2], [0, 3], [0, 4], [0, 5], [0, 7], [0, 8], [2, 3], [2, 4], [2, 5], [2, 7], [3, 6], [3, 13], [4, 12], [5, 6], [6, 9], [7, 8], [7, 9], [7, 13], [8, 10], [8, 11], [9, 10], [9, 11], [9, 14], [11, 12], [12, 14]] | undirected | none | {"Monitoring_Point_4": "0", "Temperature_Probe_1": "1", "Observation_Post_2": "2", "Humidity_Sensor_B": "3", "Grid_Cell_A2": "4", "Detector_Site_D": "5", "Soil_Monitor_B": "6", "Sample_Point_1": "7", "Sensor_Location_C": "8", "Temperature_Probe_2": "9", "Sample_Point_4": "10", "Zone_Alpha": "11", "Zone_Beta": "12", "So... | none | node_list |
real_erdos | dominating_set | sensor_network_deployment | We're setting up a wildlife monitoring network in a nature reserve. Monitoring zones are: Grid_Cell_B2, Camera_Position_1, Zone_Delta, Sample_Point_4, Observation_Post_1, Checkpoint_North, Motion_Detector_A, Wildlife_Camera_1, Camera_Position_2, Sensor_Location_C, Camera_Position_4, Detector_Site_B, Grid_Cell_A2, Water... | ["Grid_Cell_B2", "Camera_Position_1", "Wildlife_Camera_1", "Grid_Cell_A2"] | (0, 14) | [[0, 2], [0, 3], [0, 4], [0, 10], [0, 13], [1, 5], [1, 6], [1, 8], [1, 9], [1, 11], [2, 4], [2, 6], [3, 7], [3, 9], [4, 6], [4, 8], [4, 9], [4, 11], [5, 13], [6, 12], [7, 10], [7, 13], [8, 11], [10, 13], [12, 13]] | undirected | none | {"Grid_Cell_B2": "0", "Camera_Position_1": "1", "Zone_Delta": "2", "Sample_Point_4": "3", "Observation_Post_1": "4", "Checkpoint_North": "5", "Motion_Detector_A": "6", "Wildlife_Camera_1": "7", "Camera_Position_2": "8", "Sensor_Location_C": "9", "Camera_Position_4": "10", "Detector_Site_B": "11", "Grid_Cell_A2": "12", ... | none | node_list |
real_erdos | dominating_set | sensor_network_deployment | We're setting up a wildlife monitoring network in a nature reserve. Monitoring zones are: Detector_Site_D, Camera_Position_4, Checkpoint_West, Observation_Post_3, Zone_Epsilon, Observation_Post_2, Zone_Gamma, Sample_Point_3, Grid_Cell_B1, Camera_Position_1, Camera_Position_2, Air_Quality_Point_1, Humidity_Sensor_B, Wil... | ["Detector_Site_D", "Camera_Position_4", "Observation_Post_2"] | (0, 16) | [[0, 3], [0, 7], [0, 8], [0, 14], [1, 2], [1, 4], [1, 6], [1, 7], [1, 9], [1, 11], [1, 12], [1, 13], [1, 15], [2, 3], [2, 6], [2, 7], [2, 10], [3, 12], [4, 5], [4, 7], [4, 8], [5, 10], [6, 15], [7, 8], [7, 9], [7, 11], [7, 12], [8, 9], [8, 11], [9, 12], [9, 13], [9, 14], [12, 14]] | undirected | none | {"Detector_Site_D": "0", "Camera_Position_4": "1", "Checkpoint_West": "2", "Observation_Post_3": "3", "Zone_Epsilon": "4", "Observation_Post_2": "5", "Zone_Gamma": "6", "Sample_Point_3": "7", "Grid_Cell_B1": "8", "Camera_Position_1": "9", "Camera_Position_2": "10", "Air_Quality_Point_1": "11", "Humidity_Sensor_B": "12"... | none | node_list |
real_erdos | dominating_set | sensor_network_deployment | You need to deploy water quality sensors in a river network. Sampling points: Zone_Alpha, Weather_Node_1, Air_Quality_Point_1, Detector_Site_D, Grid_Cell_B1, Water_Sensor_1, Sample_Point_2, Sample_Point_3, Humidity_Sensor_A, Detector_Site_A, Grid_Cell_A1, Monitoring_Point_3, Sample_Point_1, Pollution_Monitor_A, Monitor... | ["Zone_Alpha", "Weather_Node_1", "Detector_Site_D", "Monitoring_Point_3", "Sensor_Location_D"] | (0, 20) | [[0, 2], [0, 5], [0, 6], [0, 9], [0, 12], [0, 15], [0, 18], [1, 4], [1, 10], [1, 12], [1, 14], [1, 15], [1, 16], [1, 17], [1, 18], [2, 6], [2, 8], [2, 12], [2, 18], [3, 4], [3, 5], [3, 7], [3, 8], [3, 15], [3, 18], [4, 9], [4, 11], [4, 17], [4, 18], [5, 10], [5, 18], [7, 8], [7, 9], [7, 14], [7, 16], [8, 12], [8, 14], ... | undirected | none | {"Zone_Alpha": "0", "Weather_Node_1": "1", "Air_Quality_Point_1": "2", "Detector_Site_D": "3", "Grid_Cell_B1": "4", "Water_Sensor_1": "5", "Sample_Point_2": "6", "Sample_Point_3": "7", "Humidity_Sensor_A": "8", "Detector_Site_A": "9", "Grid_Cell_A1": "10", "Monitoring_Point_3": "11", "Sample_Point_1": "12", "Pollution_... | none | node_list |
real_erdos | dominating_set | sensor_network_deployment | You're deploying environmental sensors across a monitoring area. Potential sensor locations are: Camera_Position_1, Zone_Gamma, Sensor_Location_D, Air_Quality_Point_2, Sensor_Location_B, Sample_Point_4, Monitoring_Point_3, Weather_Node_1, Air_Quality_Point_1, Soil_Monitor_B. The area connectivity is: There is a spatial... | ["Camera_Position_1", "Zone_Gamma", "Sample_Point_4"] | (0, 10) | [[0, 2], [0, 3], [0, 7], [0, 9], [1, 4], [1, 8], [2, 3], [2, 8], [3, 7], [3, 8], [5, 6], [5, 8], [6, 7]] | undirected | none | {"Camera_Position_1": "0", "Zone_Gamma": "1", "Sensor_Location_D": "2", "Air_Quality_Point_2": "3", "Sensor_Location_B": "4", "Sample_Point_4": "5", "Monitoring_Point_3": "6", "Weather_Node_1": "7", "Air_Quality_Point_1": "8", "Soil_Monitor_B": "9"} | none | node_list |
real_erdos | dominating_set | sensor_network_deployment | You need to deploy water quality sensors in a river network. Sampling points: Environmental_Station_A, Detector_Site_A, Sensor_Location_C, Environmental_Station_B, Observation_Post_2, Camera_Position_2, Sample_Point_1, Observation_Post_3, Wildlife_Camera_2, Temperature_Probe_2, Air_Quality_Point_1, Zone_Delta, Monitori... | ["Environmental_Station_A", "Detector_Site_A", "Environmental_Station_B", "Camera_Position_2", "Observation_Post_3"] | (0, 15) | [[0, 2], [0, 9], [0, 10], [0, 13], [0, 14], [1, 11], [1, 12], [2, 7], [2, 8], [2, 10], [3, 4], [3, 8], [4, 8], [4, 11], [4, 12], [4, 14], [5, 6], [5, 10], [6, 13], [7, 8], [7, 9], [8, 9], [9, 10], [9, 13], [9, 14], [10, 12], [10, 13], [10, 14], [11, 12], [11, 13], [11, 14], [13, 14]] | undirected | none | {"Environmental_Station_A": "0", "Detector_Site_A": "1", "Sensor_Location_C": "2", "Environmental_Station_B": "3", "Observation_Post_2": "4", "Camera_Position_2": "5", "Sample_Point_1": "6", "Observation_Post_3": "7", "Wildlife_Camera_2": "8", "Temperature_Probe_2": "9", "Air_Quality_Point_1": "10", "Zone_Delta": "11",... | none | node_list |
real_erdos | dominating_set | sensor_network_deployment | A smart city project requires air quality sensors. Installation points: Air_Quality_Point_1, Water_Sensor_1, Soil_Monitor_B, Temperature_Probe_2, Monitoring_Point_1, Observation_Post_2, Zone_Epsilon, Soil_Monitor_A, Motion_Detector_A, Water_Sensor_2, Checkpoint_West, Camera_Position_3, Environmental_Station_A, Detector... | ["Air_Quality_Point_1", "Monitoring_Point_1", "Zone_Epsilon", "Environmental_Station_A", "Detector_Site_B", "Zone_Alpha"] | (0, 17) | [[0, 1], [0, 2], [0, 3], [0, 7], [0, 10], [1, 4], [1, 6], [1, 14], [1, 16], [2, 3], [2, 4], [2, 5], [2, 6], [2, 7], [2, 8], [2, 10], [2, 12], [2, 13], [2, 16], [4, 5], [4, 8], [4, 9], [4, 11], [4, 13], [4, 14], [5, 9], [7, 11], [9, 15], [11, 12], [11, 15]] | undirected | none | {"Air_Quality_Point_1": "0", "Water_Sensor_1": "1", "Soil_Monitor_B": "2", "Temperature_Probe_2": "3", "Monitoring_Point_1": "4", "Observation_Post_2": "5", "Zone_Epsilon": "6", "Soil_Monitor_A": "7", "Motion_Detector_A": "8", "Water_Sensor_2": "9", "Checkpoint_West": "10", "Camera_Position_3": "11", "Environmental_Sta... | none | node_list |
real_erdos | dominating_set | sensor_network_deployment | A smart city project requires air quality sensors. Installation points: Checkpoint_South, Air_Quality_Point_1, Temperature_Probe_2, Zone_Gamma, Humidity_Sensor_A, Soil_Monitor_B, Motion_Detector_A, Motion_Detector_B, Zone_Beta, Sample_Point_1, Observation_Post_2, Monitoring_Point_4, Environmental_Station_A, Wildlife_Ca... | ["Checkpoint_South", "Air_Quality_Point_1", "Zone_Gamma", "Motion_Detector_B", "Observation_Post_2"] | (0, 18) | [[0, 2], [0, 5], [0, 6], [0, 9], [0, 11], [0, 12], [0, 14], [1, 4], [1, 8], [2, 3], [2, 17], [3, 12], [3, 15], [3, 17], [4, 6], [4, 8], [4, 10], [4, 12], [4, 13], [4, 15], [4, 17], [6, 9], [6, 10], [6, 13], [6, 14], [6, 15], [7, 12], [7, 16], [8, 9], [8, 15], [8, 17], [9, 13], [9, 17], [10, 12], [10, 13], [11, 12], [12... | undirected | none | {"Checkpoint_South": "0", "Air_Quality_Point_1": "1", "Temperature_Probe_2": "2", "Zone_Gamma": "3", "Humidity_Sensor_A": "4", "Soil_Monitor_B": "5", "Motion_Detector_A": "6", "Motion_Detector_B": "7", "Zone_Beta": "8", "Sample_Point_1": "9", "Observation_Post_2": "10", "Monitoring_Point_4": "11", "Environmental_Statio... | none | node_list |
real_erdos | dominating_set | sensor_network_deployment | You're deploying environmental sensors across a monitoring area. Potential sensor locations are: Weather_Node_1, Wildlife_Camera_2, Motion_Detector_A, Sensor_Location_C, Detector_Site_C, Sample_Point_4, Checkpoint_West, Soil_Monitor_A, Temperature_Probe_1, Monitoring_Point_4, Grid_Cell_A2. The area connectivity is: Wea... | ["Weather_Node_1", "Wildlife_Camera_2", "Motion_Detector_A", "Sensor_Location_C", "Detector_Site_C", "Checkpoint_West"] | (0, 11) | [[0, 7], [0, 8], [2, 9], [3, 5], [3, 7], [4, 5], [4, 8], [4, 10], [5, 6], [5, 8], [5, 9], [6, 7], [6, 9], [7, 8], [7, 9], [8, 9], [8, 10]] | undirected | none | {"Weather_Node_1": "0", "Wildlife_Camera_2": "1", "Motion_Detector_A": "2", "Sensor_Location_C": "3", "Detector_Site_C": "4", "Sample_Point_4": "5", "Checkpoint_West": "6", "Soil_Monitor_A": "7", "Temperature_Probe_1": "8", "Monitoring_Point_4": "9", "Grid_Cell_A2": "10"} | none | node_list |
real_erdos | dominating_set | sensor_network_deployment | You're deploying environmental sensors across a monitoring area. Potential sensor locations are: Air_Quality_Point_1, Monitoring_Point_1, Sensor_Location_B, Grid_Cell_B2, Detector_Site_C, Checkpoint_East, Humidity_Sensor_B, Camera_Position_1, Sample_Point_4, Detector_Site_D, Zone_Epsilon, Camera_Position_4, Soil_Monito... | ["Air_Quality_Point_1", "Detector_Site_C", "Camera_Position_1", "Zone_Epsilon", "Camera_Position_4", "Soil_Monitor_A"] | (0, 14) | [[0, 1], [0, 2], [0, 3], [0, 5], [0, 8], [0, 9], [1, 3], [1, 6], [1, 12], [2, 4], [2, 7], [2, 10], [3, 4], [3, 10], [4, 5], [4, 6], [4, 13], [5, 7], [5, 8], [5, 11], [6, 9], [6, 11], [6, 12], [7, 13]] | undirected | none | {"Air_Quality_Point_1": "0", "Monitoring_Point_1": "1", "Sensor_Location_B": "2", "Grid_Cell_B2": "3", "Detector_Site_C": "4", "Checkpoint_East": "5", "Humidity_Sensor_B": "6", "Camera_Position_1": "7", "Sample_Point_4": "8", "Detector_Site_D": "9", "Zone_Epsilon": "10", "Camera_Position_4": "11", "Soil_Monitor_A": "12... | none | node_list |
real_erdos | dominating_set | sensor_network_deployment | You need to deploy water quality sensors in a river network. Sampling points: Detector_Site_B, Sample_Point_1, Humidity_Sensor_A, Observation_Post_2, Sample_Point_2, Monitoring_Point_4, Environmental_Station_B, Zone_Beta, Sample_Point_3, Soil_Monitor_A, Wildlife_Camera_2, Observation_Post_1, Camera_Position_3, Sample_P... | ["Detector_Site_B", "Sample_Point_1", "Humidity_Sensor_A", "Observation_Post_2", "Sample_Point_2", "Zone_Beta", "Wildlife_Camera_2"] | (0, 15) | [[0, 8], [0, 9], [0, 13], [0, 14], [1, 6], [1, 8], [1, 11], [2, 9], [2, 13], [3, 5], [4, 6], [4, 8], [5, 8], [5, 12], [7, 14], [8, 11], [9, 10], [9, 13], [10, 11], [10, 12], [10, 13], [11, 14], [12, 13]] | undirected | none | {"Detector_Site_B": "0", "Sample_Point_1": "1", "Humidity_Sensor_A": "2", "Observation_Post_2": "3", "Sample_Point_2": "4", "Monitoring_Point_4": "5", "Environmental_Station_B": "6", "Zone_Beta": "7", "Sample_Point_3": "8", "Soil_Monitor_A": "9", "Wildlife_Camera_2": "10", "Observation_Post_1": "11", "Camera_Position_3... | none | node_list |
real_erdos | dominating_set | sensor_network_deployment | You need to deploy water quality sensors in a river network. Sampling points: Water_Sensor_2, Observation_Post_2, Zone_Alpha, Monitoring_Point_3, Pollution_Monitor_A, Wildlife_Camera_2, Detector_Site_A, Sensor_Location_C, Sensor_Location_B, Sensor_Location_A, Observation_Post_1, Sample_Point_3, Detector_Site_B, Zone_Ga... | ["Water_Sensor_2", "Wildlife_Camera_2", "Sensor_Location_C", "Sensor_Location_B", "Sensor_Location_A", "Observation_Post_1", "Zone_Gamma", "Camera_Position_4", "Checkpoint_East"] | (0, 16) | [[0, 1], [0, 2], [0, 3], [0, 4], [0, 12], [1, 3], [1, 6], [1, 8], [1, 9], [1, 10], [2, 4], [2, 5], [2, 7], [2, 12], [2, 13], [2, 14], [3, 5], [3, 8], [3, 14], [3, 15], [4, 7], [4, 11], [4, 15], [5, 6], [6, 9], [6, 10], [6, 13], [9, 11]] | undirected | none | {"Water_Sensor_2": "0", "Observation_Post_2": "1", "Zone_Alpha": "2", "Monitoring_Point_3": "3", "Pollution_Monitor_A": "4", "Wildlife_Camera_2": "5", "Detector_Site_A": "6", "Sensor_Location_C": "7", "Sensor_Location_B": "8", "Sensor_Location_A": "9", "Observation_Post_1": "10", "Sample_Point_3": "11", "Detector_Site_... | none | node_list |
real_erdos | dominating_set | sensor_network_deployment | We're setting up a wildlife monitoring network in a nature reserve. Monitoring zones are: Air_Quality_Point_2, Motion_Detector_A, Environmental_Station_B, Camera_Position_4, Checkpoint_East, Sample_Point_3, Monitoring_Point_3, Detector_Site_C, Sensor_Location_B, Observation_Post_1, Camera_Position_1, Detector_Site_D, H... | ["Air_Quality_Point_2", "Motion_Detector_A", "Environmental_Station_B", "Checkpoint_East", "Sample_Point_3", "Detector_Site_C", "Observation_Post_1"] | (0, 20) | [[0, 8], [0, 10], [0, 12], [1, 8], [1, 11], [1, 17], [2, 3], [2, 11], [2, 12], [2, 14], [2, 16], [3, 11], [3, 17], [4, 6], [4, 12], [4, 15], [5, 12], [5, 13], [5, 18], [6, 8], [6, 14], [6, 16], [7, 15], [8, 14], [8, 18], [9, 16], [9, 19], [10, 11], [10, 14], [11, 12], [11, 14], [12, 13], [12, 15], [12, 16], [14, 15], [... | undirected | none | {"Air_Quality_Point_2": "0", "Motion_Detector_A": "1", "Environmental_Station_B": "2", "Camera_Position_4": "3", "Checkpoint_East": "4", "Sample_Point_3": "5", "Monitoring_Point_3": "6", "Detector_Site_C": "7", "Sensor_Location_B": "8", "Observation_Post_1": "9", "Camera_Position_1": "10", "Detector_Site_D": "11", "Hum... | none | node_list |
real_erdos | dominating_set | sensor_network_deployment | We're setting up a wildlife monitoring network in a nature reserve. Monitoring zones are: Zone_Delta, Zone_Alpha, Checkpoint_West, Grid_Cell_B2, Motion_Detector_B, Camera_Position_2, Zone_Beta, Humidity_Sensor_A, Zone_Epsilon, Observation_Post_3, Water_Sensor_2, Soil_Monitor_B, Detector_Site_C, Zone_Gamma, Grid_Cell_A2... | ["Zone_Delta", "Zone_Alpha", "Checkpoint_West", "Grid_Cell_B2", "Humidity_Sensor_A", "Zone_Epsilon", "Zone_Gamma", "Grid_Cell_A2"] | (0, 15) | [[0, 4], [0, 9], [0, 10], [1, 4], [1, 6], [1, 12], [2, 5], [2, 11], [2, 12], [3, 11], [4, 5], [4, 8], [4, 11], [4, 13], [5, 12], [5, 13], [6, 7], [6, 11], [6, 14], [7, 10], [7, 11], [8, 10], [8, 11], [8, 12], [9, 11], [9, 13], [10, 13], [10, 14], [11, 13], [11, 14]] | undirected | none | {"Zone_Delta": "0", "Zone_Alpha": "1", "Checkpoint_West": "2", "Grid_Cell_B2": "3", "Motion_Detector_B": "4", "Camera_Position_2": "5", "Zone_Beta": "6", "Humidity_Sensor_A": "7", "Zone_Epsilon": "8", "Observation_Post_3": "9", "Water_Sensor_2": "10", "Soil_Monitor_B": "11", "Detector_Site_C": "12", "Zone_Gamma": "13",... | none | node_list |
real_erdos | dominating_set | sensor_network_deployment | You need to deploy water quality sensors in a river network. Sampling points: Camera_Position_3, Zone_Delta, Sample_Point_4, Zone_Alpha, Humidity_Sensor_A, Soil_Monitor_A, Zone_Epsilon, Detector_Site_A, with water flow connections: Camera_Position_3 is within sensing range of Sample_Point_4. There is a spatial connecti... | ["Camera_Position_3", "Zone_Delta"] | (0, 8) | [[0, 2], [0, 3], [0, 5], [1, 4], [1, 6], [1, 7], [2, 6], [4, 7], [5, 6], [6, 7]] | undirected | none | {"Camera_Position_3": "0", "Zone_Delta": "1", "Sample_Point_4": "2", "Zone_Alpha": "3", "Humidity_Sensor_A": "4", "Soil_Monitor_A": "5", "Zone_Epsilon": "6", "Detector_Site_A": "7"} | none | node_list |
real_erdos | dominating_set | sensor_network_deployment | We're setting up a wildlife monitoring network in a nature reserve. Monitoring zones are: Wildlife_Camera_2, Grid_Cell_B1, Monitoring_Point_2, Pollution_Monitor_A, Water_Sensor_2, Monitoring_Point_3, Checkpoint_East, Camera_Position_3, Sensor_Location_C, Sample_Point_4, Motion_Detector_B, Weather_Node_1, connected as: ... | ["Wildlife_Camera_2", "Grid_Cell_B1", "Pollution_Monitor_A", "Camera_Position_3", "Sample_Point_4"] | (0, 12) | [[0, 2], [0, 5], [1, 4], [2, 3], [2, 4], [2, 5], [2, 6], [2, 10], [3, 6], [3, 8], [4, 9], [5, 6], [5, 9], [5, 11], [7, 10], [7, 11], [8, 11], [10, 11]] | undirected | none | {"Wildlife_Camera_2": "0", "Grid_Cell_B1": "1", "Monitoring_Point_2": "2", "Pollution_Monitor_A": "3", "Water_Sensor_2": "4", "Monitoring_Point_3": "5", "Checkpoint_East": "6", "Camera_Position_3": "7", "Sensor_Location_C": "8", "Sample_Point_4": "9", "Motion_Detector_B": "10", "Weather_Node_1": "11"} | none | node_list |
real_erdos | dominating_set | social_network_influencers | You're analyzing a professional network to find opinion leaders. The network consists of: Frank, Uma, Follower_B, Expert_1, Vlogger_Y, Olivia, Opinion_Leader_B, Zack, Power_User_1, David, Wendy, Steve, Peter, Grace, Influencer_A, Jack, User_102, User_101, Maria, Xavier, with connections: Frank and Uma are directly link... | ["Frank", "Expert_1", "Opinion_Leader_B", "Peter", "Xavier"] | (0, 20) | [[0, 1], [0, 2], [0, 4], [0, 17], [1, 3], [1, 6], [1, 12], [1, 13], [1, 15], [1, 18], [2, 4], [2, 6], [2, 7], [2, 9], [2, 10], [2, 14], [2, 17], [2, 18], [3, 4], [3, 5], [3, 7], [3, 8], [3, 10], [3, 16], [4, 5], [4, 13], [4, 17], [5, 12], [5, 14], [6, 7], [6, 8], [6, 9], [6, 11], [6, 13], [6, 15], [6, 17], [6, 18], [7,... | undirected | none | {"Frank": "0", "Uma": "1", "Follower_B": "2", "Expert_1": "3", "Vlogger_Y": "4", "Olivia": "5", "Opinion_Leader_B": "6", "Zack": "7", "Power_User_1": "8", "David": "9", "Wendy": "10", "Steve": "11", "Peter": "12", "Grace": "13", "Influencer_A": "14", "Jack": "15", "User_102": "16", "User_101": "17", "Maria": "18", "Xav... | none | node_list |
real_erdos | dominating_set | social_network_influencers | You're analyzing a professional network to find opinion leaders. The network consists of: Uma, Carol, Creator_2, Isabel, David, Follower_A, Alice, Member_Alpha, Victor, Peter, Celebrity_B, Tina, with connections: Uma is connected to David. There is a friendship between Carol and Alice. There is a friendship between Cre... | ["Uma", "Carol", "Creator_2", "Isabel", "Follower_A", "Celebrity_B"] | (0, 12) | [[0, 4], [1, 6], [2, 4], [2, 9], [2, 11], [3, 7], [3, 11], [4, 5], [4, 6], [4, 8], [5, 8], [6, 10], [7, 9], [8, 9], [8, 10], [8, 11]] | undirected | none | {"Uma": "0", "Carol": "1", "Creator_2": "2", "Isabel": "3", "David": "4", "Follower_A": "5", "Alice": "6", "Member_Alpha": "7", "Victor": "8", "Peter": "9", "Celebrity_B": "10", "Tina": "11"} | none | node_list |
real_erdos | dominating_set | social_network_influencers | A marketing team wants to identify key influencers in a social network to maximize campaign reach. The network members are: Nathan, Tina, Power_User_1, Influencer_B, Maria, Jack, David, Leo, Quinn. The friendship connections are: Nathan is connected to David. Tina and Power_User_1 are directly linked in the social grap... | ["Nathan", "Tina", "Influencer_B", "Maria", "Quinn"] | (0, 9) | [[0, 6], [1, 2], [1, 6], [1, 7], [2, 6], [2, 7], [4, 5], [4, 7], [5, 8], [6, 7]] | undirected | none | {"Nathan": "0", "Tina": "1", "Power_User_1": "2", "Influencer_B": "3", "Maria": "4", "Jack": "5", "David": "6", "Leo": "7", "Quinn": "8"} | none | node_list |
real_erdos | dominating_set | social_network_influencers | We're studying information diffusion in an online community. Community members: Expert_2, Creator_2, User_104, Frank, Power_User_1, Blogger_X, Maria, Follower_B, Wendy, Zack, Opinion_Leader_B, Member_Beta, Vlogger_Y, Community_Leader_2, User_103, with interactions: There is a friendship between Expert_2 and Frank. Expe... | ["Expert_2", "Creator_2", "User_104", "Power_User_1", "Maria", "Follower_B"] | (0, 15) | [[0, 3], [0, 10], [0, 12], [0, 14], [1, 13], [2, 5], [2, 8], [2, 10], [2, 11], [3, 8], [4, 5], [4, 8], [5, 11], [5, 12], [6, 9], [6, 14], [8, 9], [8, 13], [9, 11], [10, 12], [11, 12], [13, 14]] | undirected | none | {"Expert_2": "0", "Creator_2": "1", "User_104": "2", "Frank": "3", "Power_User_1": "4", "Blogger_X": "5", "Maria": "6", "Follower_B": "7", "Wendy": "8", "Zack": "9", "Opinion_Leader_B": "10", "Member_Beta": "11", "Vlogger_Y": "12", "Community_Leader_2": "13", "User_103": "14"} | none | node_list |
real_erdos | dominating_set | social_network_influencers | We're studying information diffusion in an online community. Community members: Henry, Victor, Influencer_B, Yara, Member_Beta, Celebrity_B, Creator_2, Bob, Follower_B, Expert_2, Community_Leader_2, Influencer_A, Steve, Grace, Opinion_Leader_A, User_101, Peter, Kate, with interactions: Henry has Victor as a direct cont... | ["Henry", "Influencer_B", "Member_Beta", "Follower_B", "User_101"] | (0, 18) | [[0, 1], [0, 3], [0, 5], [0, 7], [0, 9], [1, 5], [1, 6], [1, 8], [1, 10], [1, 12], [1, 14], [1, 15], [2, 9], [2, 11], [2, 12], [2, 14], [3, 5], [3, 10], [3, 12], [3, 17], [4, 5], [4, 6], [4, 7], [4, 9], [4, 10], [4, 13], [5, 8], [5, 13], [5, 17], [6, 10], [6, 11], [6, 16], [6, 17], [7, 11], [7, 13], [7, 16], [8, 17], [... | undirected | none | {"Henry": "0", "Victor": "1", "Influencer_B": "2", "Yara": "3", "Member_Beta": "4", "Celebrity_B": "5", "Creator_2": "6", "Bob": "7", "Follower_B": "8", "Expert_2": "9", "Community_Leader_2": "10", "Influencer_A": "11", "Steve": "12", "Grace": "13", "Opinion_Leader_A": "14", "User_101": "15", "Peter": "16", "Kate": "17... | none | node_list |
real_erdos | dominating_set | social_network_influencers | We're studying information diffusion in an online community. Community members: Celebrity_A, Creator_2, User_104, Opinion_Leader_A, Celebrity_B, Isabel, Member_Alpha, Leo, Member_Beta, Jack, Follower_A, Carol, Influencer_A, Kate, Peter, with interactions: Celebrity_A has Opinion_Leader_A as a direct contact. Celebrity_... | ["Celebrity_A", "Creator_2", "User_104", "Isabel", "Follower_A", "Influencer_A", "Kate"] | (0, 15) | [[0, 3], [0, 4], [0, 7], [0, 9], [1, 4], [1, 6], [1, 8], [1, 14], [3, 5], [3, 8], [3, 12], [4, 9], [5, 8], [5, 9], [6, 10], [6, 11], [7, 8], [7, 12], [8, 9], [8, 10], [8, 12], [9, 11], [9, 12], [10, 11], [11, 14]] | undirected | none | {"Celebrity_A": "0", "Creator_2": "1", "User_104": "2", "Opinion_Leader_A": "3", "Celebrity_B": "4", "Isabel": "5", "Member_Alpha": "6", "Leo": "7", "Member_Beta": "8", "Jack": "9", "Follower_A": "10", "Carol": "11", "Influencer_A": "12", "Kate": "13", "Peter": "14"} | none | node_list |
real_erdos | dominating_set | social_network_influencers | A marketing team wants to identify key influencers in a social network to maximize campaign reach. The network members are: Follower_B, User_102, Quinn, Expert_2, User_101, Xavier, Community_Leader_1, Peter, Bob, Vlogger_Y, Follower_A, Member_Beta, Community_Leader_2. The friendship connections are: Follower_B and User... | ["Follower_B", "Quinn", "Vlogger_Y", "Follower_A"] | (0, 13) | [[0, 1], [0, 4], [0, 5], [0, 7], [0, 8], [1, 3], [1, 4], [1, 6], [1, 12], [2, 3], [2, 6], [2, 11], [3, 8], [4, 6], [4, 8], [5, 9], [6, 10], [7, 10], [9, 12]] | undirected | none | {"Follower_B": "0", "User_102": "1", "Quinn": "2", "Expert_2": "3", "User_101": "4", "Xavier": "5", "Community_Leader_1": "6", "Peter": "7", "Bob": "8", "Vlogger_Y": "9", "Follower_A": "10", "Member_Beta": "11", "Community_Leader_2": "12"} | none | node_list |
real_erdos | dominating_set | social_network_influencers | We're studying information diffusion in an online community. Community members: User_102, Leo, Frank, Alice, Influencer_B, Follower_A, Blogger_X, Quinn, Jack, Xavier, Follower_B, Opinion_Leader_A, User_104, with interactions: There is a friendship between User_102 and Blogger_X. User_102 follows Xavier. There is a frie... | ["User_102", "Leo", "Frank", "Alice", "Influencer_B"] | (0, 13) | [[0, 6], [0, 9], [0, 10], [0, 11], [0, 12], [1, 7], [2, 5], [2, 7], [2, 8], [2, 11], [3, 5], [3, 6], [4, 6], [4, 7], [4, 9], [4, 10], [4, 11], [5, 9], [9, 11], [9, 12]] | undirected | none | {"User_102": "0", "Leo": "1", "Frank": "2", "Alice": "3", "Influencer_B": "4", "Follower_A": "5", "Blogger_X": "6", "Quinn": "7", "Jack": "8", "Xavier": "9", "Follower_B": "10", "Opinion_Leader_A": "11", "User_104": "12"} | none | node_list |
real_erdos | dominating_set | social_network_influencers | A social media platform wants to seed a viral campaign. Users in the network are: Bob, Blogger_X, User_104, Peter, Frank, User_102, Uma, Olivia. The follower relationships are: Bob and Blogger_X are directly linked in the social graph. Bob is connected to Peter. Bob is connected to User_102. Bob follows Uma. Blogger_X ... | ["Bob", "User_104", "Frank", "Olivia"] | (0, 8) | [[0, 1], [0, 3], [0, 5], [0, 6], [1, 7], [2, 3], [3, 4], [3, 7], [4, 6], [5, 6], [5, 7], [6, 7]] | undirected | none | {"Bob": "0", "Blogger_X": "1", "User_104": "2", "Peter": "3", "Frank": "4", "User_102": "5", "Uma": "6", "Olivia": "7"} | none | node_list |
real_erdos | dominating_set | social_network_influencers | You're analyzing a professional network to find opinion leaders. The network consists of: Zack, Creator_2, Xavier, Peter, Maria, Influencer_A, Member_Beta, Wendy, User_103, Grace, Bob, Nathan, Community_Leader_1, Frank, Power_User_1, Rachel, David, Influencer_B, Alice, Yara, with connections: Zack has Creator_2 as a di... | ["Zack", "Xavier", "Member_Beta", "Wendy", "Grace", "Bob", "Power_User_1", "David", "Yara"] | (0, 20) | [[0, 1], [0, 3], [0, 5], [0, 11], [0, 18], [1, 15], [2, 4], [2, 12], [2, 17], [3, 5], [3, 6], [3, 9], [3, 11], [4, 11], [5, 8], [5, 14], [5, 18], [5, 19], [6, 8], [6, 13], [7, 17], [8, 9], [8, 11], [8, 12], [9, 12], [9, 13], [10, 15], [12, 13], [12, 15], [15, 18], [15, 19], [17, 19]] | undirected | none | {"Zack": "0", "Creator_2": "1", "Xavier": "2", "Peter": "3", "Maria": "4", "Influencer_A": "5", "Member_Beta": "6", "Wendy": "7", "User_103": "8", "Grace": "9", "Bob": "10", "Nathan": "11", "Community_Leader_1": "12", "Frank": "13", "Power_User_1": "14", "Rachel": "15", "David": "16", "Influencer_B": "17", "Alice": "18... | none | node_list |
real_erdos | dominating_set | social_network_influencers | You're analyzing a professional network to find opinion leaders. The network consists of: Uma, Opinion_Leader_A, Nathan, User_102, Power_User_1, Vlogger_Y, Creator_1, Frank, Grace, Blogger_X, Kate, Celebrity_A, Xavier, Expert_2, Henry, Isabel, Opinion_Leader_B, Alice, with connections: There is a friendship between Uma... | ["Uma", "Opinion_Leader_A", "Nathan", "Frank"] | (0, 18) | [[0, 6], [0, 8], [0, 10], [0, 11], [0, 14], [0, 16], [0, 17], [1, 3], [1, 4], [1, 9], [1, 14], [2, 3], [2, 5], [2, 6], [2, 8], [2, 9], [2, 13], [2, 15], [2, 17], [3, 5], [3, 13], [3, 14], [3, 15], [3, 17], [4, 5], [4, 10], [4, 11], [4, 13], [5, 8], [5, 10], [5, 11], [5, 14], [5, 16], [6, 9], [6, 10], [6, 12], [6, 16], ... | undirected | none | {"Uma": "0", "Opinion_Leader_A": "1", "Nathan": "2", "User_102": "3", "Power_User_1": "4", "Vlogger_Y": "5", "Creator_1": "6", "Frank": "7", "Grace": "8", "Blogger_X": "9", "Kate": "10", "Celebrity_A": "11", "Xavier": "12", "Expert_2": "13", "Henry": "14", "Isabel": "15", "Opinion_Leader_B": "16", "Alice": "17"} | none | node_list |
real_erdos | dominating_set | social_network_influencers | You're analyzing a professional network to find opinion leaders. The network consists of: Isabel, Follower_B, Creator_1, Creator_2, User_104, Kate, Vlogger_Y, Yara, User_102, Nathan, Community_Leader_1, with connections: There is a friendship between Isabel and Creator_2. Isabel is connected to Kate. Isabel has Vlogger... | ["Isabel", "Follower_B", "User_104", "Nathan", "Community_Leader_1"] | (0, 11) | [[0, 3], [0, 5], [0, 6], [0, 7], [0, 8], [1, 2], [2, 5], [2, 6], [2, 8], [2, 9], [2, 10], [3, 6], [3, 8], [3, 10], [4, 8], [5, 10], [6, 9], [6, 10], [7, 8], [7, 10]] | undirected | none | {"Isabel": "0", "Follower_B": "1", "Creator_1": "2", "Creator_2": "3", "User_104": "4", "Kate": "5", "Vlogger_Y": "6", "Yara": "7", "User_102": "8", "Nathan": "9", "Community_Leader_1": "10"} | none | node_list |
real_erdos | dominating_set | social_network_influencers | We're studying information diffusion in an online community. Community members: Power_User_2, Quinn, User_104, Carol, Bob, Uma, Celebrity_B, Follower_A, Kate, Isabel, Jack, David, Creator_2, User_101, with interactions: Power_User_2 follows Quinn. Power_User_2 and Uma are directly linked in the social graph. Power_User... | ["Power_User_2", "User_104", "Carol", "Bob", "Follower_A", "David", "User_101"] | (0, 14) | [[0, 1], [0, 5], [0, 6], [0, 9], [1, 7], [1, 8], [1, 12], [1, 13], [3, 12], [4, 8], [4, 9], [5, 6], [5, 7], [5, 8], [5, 10], [5, 11], [5, 13], [6, 7], [6, 11], [6, 13], [7, 9], [7, 10], [8, 9], [8, 10], [8, 12], [9, 10], [10, 11], [11, 12], [12, 13]] | undirected | none | {"Power_User_2": "0", "Quinn": "1", "User_104": "2", "Carol": "3", "Bob": "4", "Uma": "5", "Celebrity_B": "6", "Follower_A": "7", "Kate": "8", "Isabel": "9", "Jack": "10", "David": "11", "Creator_2": "12", "User_101": "13"} | none | node_list |
real_erdos | dominating_set | social_network_influencers | You're analyzing a professional network to find opinion leaders. The network consists of: Blogger_X, Celebrity_B, Alice, Vlogger_Y, David, Emma, User_102, Yara, Jack, Influencer_A, Victor, Xavier, Creator_2, Steve, Carol, Expert_2, Opinion_Leader_A, User_104, Leo, Expert_1, with connections: Blogger_X has Alice as a di... | ["Blogger_X", "Celebrity_B", "Vlogger_Y", "David", "Influencer_A", "Expert_1"] | (0, 20) | [[0, 2], [0, 8], [0, 10], [0, 11], [0, 13], [1, 6], [1, 12], [1, 14], [1, 15], [2, 3], [2, 18], [2, 19], [3, 5], [3, 11], [3, 18], [4, 7], [4, 11], [4, 13], [4, 16], [4, 18], [5, 6], [5, 13], [5, 19], [6, 13], [6, 14], [6, 16], [6, 19], [7, 13], [7, 14], [7, 15], [7, 16], [7, 18], [7, 19], [8, 10], [8, 15], [8, 17], [9... | undirected | none | {"Blogger_X": "0", "Celebrity_B": "1", "Alice": "2", "Vlogger_Y": "3", "David": "4", "Emma": "5", "User_102": "6", "Yara": "7", "Jack": "8", "Influencer_A": "9", "Victor": "10", "Xavier": "11", "Creator_2": "12", "Steve": "13", "Carol": "14", "Expert_2": "15", "Opinion_Leader_A": "16", "User_104": "17", "Leo": "18", "E... | none | node_list |
real_erdos | dominating_set | social_network_influencers | A marketing team wants to identify key influencers in a social network to maximize campaign reach. The network members are: Jack, User_104, Tina, Power_User_2, Community_Leader_2, User_101, Opinion_Leader_B, Peter, Quinn, Celebrity_A, Grace, Nathan, Creator_2, Vlogger_Y, Xavier, Frank. The friendship connections are: J... | ["Jack", "User_104", "Tina", "Peter", "Grace", "Creator_2"] | (0, 16) | [[0, 3], [0, 4], [0, 5], [0, 6], [0, 11], [0, 15], [1, 6], [1, 13], [1, 14], [1, 15], [2, 9], [3, 4], [3, 5], [3, 14], [4, 7], [4, 12], [6, 7], [6, 12], [7, 8], [10, 15], [12, 14], [13, 15]] | undirected | none | {"Jack": "0", "User_104": "1", "Tina": "2", "Power_User_2": "3", "Community_Leader_2": "4", "User_101": "5", "Opinion_Leader_B": "6", "Peter": "7", "Quinn": "8", "Celebrity_A": "9", "Grace": "10", "Nathan": "11", "Creator_2": "12", "Vlogger_Y": "13", "Xavier": "14", "Frank": "15"} | none | node_list |
real_erdos | dominating_set | social_network_influencers | You're analyzing a professional network to find opinion leaders. The network consists of: Influencer_B, Creator_2, Opinion_Leader_A, User_103, Leo, Member_Beta, Community_Leader_2, Follower_A, Tina, Peter, Nathan, Yara, with connections: Influencer_B and Community_Leader_2 are directly linked in the social graph. Creat... | ["Influencer_B", "Creator_2", "Opinion_Leader_A", "Tina", "Nathan"] | (0, 12) | [[0, 6], [1, 3], [1, 5], [1, 11], [2, 4], [2, 5], [2, 7], [2, 9], [3, 8], [4, 6], [4, 7], [5, 6], [6, 7], [7, 9], [8, 11]] | undirected | none | {"Influencer_B": "0", "Creator_2": "1", "Opinion_Leader_A": "2", "User_103": "3", "Leo": "4", "Member_Beta": "5", "Community_Leader_2": "6", "Follower_A": "7", "Tina": "8", "Peter": "9", "Nathan": "10", "Yara": "11"} | none | node_list |
real_erdos | dominating_set | social_network_influencers | A marketing team wants to identify key influencers in a social network to maximize campaign reach. The network members are: Expert_2, Power_User_2, Vlogger_Y, Influencer_B, Creator_2, Member_Alpha, Bob, Carol, Jack, Grace, Henry, Emma, Steve, Leo, User_103, Uma, Celebrity_B, User_104, Alice, Nathan. The friendship conn... | ["Expert_2", "Grace", "Henry", "User_104", "Nathan"] | (0, 20) | [[0, 1], [0, 2], [0, 3], [0, 4], [0, 5], [0, 6], [0, 7], [0, 8], [0, 12], [0, 14], [0, 16], [1, 4], [1, 5], [1, 8], [1, 9], [1, 11], [1, 17], [1, 19], [2, 15], [3, 4], [3, 7], [3, 10], [4, 5], [4, 6], [4, 7], [4, 9], [4, 16], [4, 18], [5, 6], [5, 8], [5, 14], [5, 17], [6, 9], [6, 13], [6, 15], [6, 18], [6, 19], [7, 10]... | undirected | none | {"Expert_2": "0", "Power_User_2": "1", "Vlogger_Y": "2", "Influencer_B": "3", "Creator_2": "4", "Member_Alpha": "5", "Bob": "6", "Carol": "7", "Jack": "8", "Grace": "9", "Henry": "10", "Emma": "11", "Steve": "12", "Leo": "13", "User_103": "14", "Uma": "15", "Celebrity_B": "16", "User_104": "17", "Alice": "18", "Nathan"... | none | node_list |
real_erdos | dominating_set | social_network_influencers | A marketing team wants to identify key influencers in a social network to maximize campaign reach. The network members are: Henry, Peter, Jack, Expert_2, Tina, Frank, Creator_1, Expert_1, Grace, Influencer_A, Alice, Isabel, Wendy, Leo, Victor, Steve. The friendship connections are: There is a friendship between Henry a... | ["Henry", "Creator_1", "Alice", "Wendy", "Leo", "Victor"] | (0, 16) | [[0, 1], [0, 2], [0, 3], [0, 4], [0, 5], [0, 7], [0, 9], [0, 11], [1, 3], [1, 4], [1, 5], [1, 6], [1, 7], [1, 10], [1, 11], [1, 12], [1, 14], [3, 6], [3, 8], [3, 9], [3, 13], [4, 12], [4, 13], [4, 15], [5, 10], [5, 14], [6, 8], [12, 15]] | undirected | none | {"Henry": "0", "Peter": "1", "Jack": "2", "Expert_2": "3", "Tina": "4", "Frank": "5", "Creator_1": "6", "Expert_1": "7", "Grace": "8", "Influencer_A": "9", "Alice": "10", "Isabel": "11", "Wendy": "12", "Leo": "13", "Victor": "14", "Steve": "15"} | none | node_list |
real_erdos | dominating_set | social_network_influencers | A marketing team wants to identify key influencers in a social network to maximize campaign reach. The network members are: Isabel, Follower_B, Expert_2, Wendy, Expert_1, Bob, Power_User_2, Alice, Tina. The friendship connections are: Isabel and Wendy are directly linked in the social graph. Isabel and Bob are directly... | ["Isabel", "Follower_B"] | (0, 9) | [[0, 3], [0, 5], [0, 7], [0, 8], [1, 2], [1, 4], [1, 6], [1, 7], [1, 8], [2, 4], [2, 7], [3, 5], [4, 5], [4, 8], [5, 6], [6, 7]] | undirected | none | {"Isabel": "0", "Follower_B": "1", "Expert_2": "2", "Wendy": "3", "Expert_1": "4", "Bob": "5", "Power_User_2": "6", "Alice": "7", "Tina": "8"} | none | node_list |
real_erdos | dominating_set | social_network_influencers | We're studying information diffusion in an online community. Community members: Quinn, Tina, Follower_B, User_102, Opinion_Leader_B, Uma, Maria, Expert_1, Victor, User_104, David, Member_Alpha, Power_User_1, Zack, Vlogger_Y, Member_Beta, Follower_A, with interactions: Quinn follows Victor. Quinn follows Member_Beta. Ti... | ["Quinn", "Tina", "Follower_B", "Uma", "Expert_1", "Zack", "Follower_A"] | (0, 17) | [[0, 8], [0, 15], [1, 3], [1, 4], [1, 6], [1, 10], [1, 11], [1, 15], [2, 9], [2, 12], [3, 8], [5, 14], [6, 10], [6, 16], [8, 10], [8, 12], [9, 15], [10, 16], [11, 14], [12, 16], [15, 16]] | undirected | none | {"Quinn": "0", "Tina": "1", "Follower_B": "2", "User_102": "3", "Opinion_Leader_B": "4", "Uma": "5", "Maria": "6", "Expert_1": "7", "Victor": "8", "User_104": "9", "David": "10", "Member_Alpha": "11", "Power_User_1": "12", "Zack": "13", "Vlogger_Y": "14", "Member_Beta": "15", "Follower_A": "16"} | none | node_list |
real_erdos | dominating_set | wireless_network_coverage | We're optimizing a cellular network deployment. The candidate cell tower sites are: Receiver_Station_B, Transmitter_2, Signal_Point_B, Relay_Node_2, WiFi_Hub_B, Broadcast_Point_2, Access_Point_1, Access_Point_4, Relay_Node_5, with the following connectivity: There is a wireless link between Receiver_Station_B and Relay... | ["Receiver_Station_B", "Transmitter_2", "Broadcast_Point_2"] | (0, 9) | [[0, 3], [0, 4], [1, 2], [1, 4], [1, 7], [1, 8], [2, 5], [4, 5], [5, 6]] | undirected | none | {"Receiver_Station_B": "0", "Transmitter_2": "1", "Signal_Point_B": "2", "Relay_Node_2": "3", "WiFi_Hub_B": "4", "Broadcast_Point_2": "5", "Access_Point_1": "6", "Access_Point_4": "7", "Relay_Node_5": "8"} | none | node_list |
real_erdos | dominating_set | wireless_network_coverage | A telecommunications company needs to deploy WiFi access points across a campus. Available locations are: Relay_Node_5, Mobile_Tower_B, Router_Location_2, Wireless_Station_2, Base_Station_South, Relay_Node_4, Tower_C, Receiver_Station_A, Coverage_Zone_1, Relay_Node_2, Tower_B, WiFi_Hub_A, Access_Point_1, Network_Node_A... | ["Relay_Node_5", "Tower_B", "WiFi_Hub_A", "Access_Point_1", "Network_Node_A"] | (0, 14) | [[0, 1], [0, 2], [0, 3], [0, 4], [0, 5], [0, 6], [0, 7], [0, 8], [0, 9], [1, 3], [2, 4], [2, 5], [2, 6], [2, 7], [2, 11], [2, 12], [3, 8], [3, 11], [3, 12], [3, 13], [5, 9], [5, 13], [6, 10], [8, 10]] | undirected | none | {"Relay_Node_5": "0", "Mobile_Tower_B": "1", "Router_Location_2": "2", "Wireless_Station_2": "3", "Base_Station_South": "4", "Relay_Node_4": "5", "Tower_C": "6", "Receiver_Station_A": "7", "Coverage_Zone_1": "8", "Relay_Node_2": "9", "Tower_B": "10", "WiFi_Hub_A": "11", "Access_Point_1": "12", "Network_Node_A": "13"} | none | node_list |
real_erdos | dominating_set | wireless_network_coverage | You are designing a wireless network to cover a large area. The network consists of potential tower locations: Relay_Node_2, Coverage_Zone_2, Access_Point_3, WiFi_Hub_C, Tower_F, Broadcast_Point_1, Base_Station_North, Hotspot_A, Coverage_Zone_1, Wireless_Station_2, Base_Station_East, Tower_D, Antenna_Site_Gamma, Cell_T... | ["Relay_Node_2", "Access_Point_3", "Hotspot_A", "Wireless_Station_2", "Antenna_Site_Gamma", "Cell_Tower_2", "Access_Point_5"] | (0, 19) | [[0, 1], [0, 3], [0, 4], [0, 11], [0, 16], [1, 6], [1, 8], [1, 9], [1, 11], [1, 17], [2, 3], [2, 5], [2, 6], [2, 8], [3, 6], [3, 7], [3, 10], [3, 18], [4, 5], [4, 9], [4, 10], [4, 13], [5, 9], [6, 12], [7, 10], [8, 16], [8, 17], [9, 16], [10, 12], [11, 13], [11, 14], [11, 16], [12, 15], [12, 18], [13, 15], [13, 16], [1... | undirected | none | {"Relay_Node_2": "0", "Coverage_Zone_2": "1", "Access_Point_3": "2", "WiFi_Hub_C": "3", "Tower_F": "4", "Broadcast_Point_1": "5", "Base_Station_North": "6", "Hotspot_A": "7", "Coverage_Zone_1": "8", "Wireless_Station_2": "9", "Base_Station_East": "10", "Tower_D": "11", "Antenna_Site_Gamma": "12", "Cell_Tower_2": "13", ... | none | node_list |
real_erdos | dominating_set | wireless_network_coverage | You need to establish wireless coverage for an IoT network. The potential relay nodes are: Antenna_Site_Beta, Antenna_Site_Alpha, Tower_D, Router_Location_2, Transmitter_1, Broadcast_Point_2, Relay_Node_3, Hotspot_B, Base_Station_East, Tower_G. The network topology is: Antenna_Site_Beta can communicate directly with An... | ["Antenna_Site_Beta", "Tower_D", "Router_Location_2", "Transmitter_1", "Relay_Node_3", "Base_Station_East"] | (0, 10) | [[0, 1], [0, 5], [0, 9], [1, 5], [1, 6], [1, 7], [1, 8], [1, 9], [2, 7], [3, 9], [5, 7], [6, 7], [6, 9]] | undirected | none | {"Antenna_Site_Beta": "0", "Antenna_Site_Alpha": "1", "Tower_D": "2", "Router_Location_2": "3", "Transmitter_1": "4", "Broadcast_Point_2": "5", "Relay_Node_3": "6", "Hotspot_B": "7", "Base_Station_East": "8", "Tower_G": "9"} | none | node_list |
real_erdos | dominating_set | wireless_network_coverage | You need to establish wireless coverage for an IoT network. The potential relay nodes are: Receiver_Station_B, Network_Node_A, Access_Point_1, Receiver_Station_A, Coverage_Zone_1, Tower_E, Access_Point_2, Signal_Point_B, Relay_Node_5, Broadcast_Point_2, Router_Location_2, WiFi_Hub_A, Hotspot_A. The network topology is:... | ["Receiver_Station_B", "Network_Node_A", "Receiver_Station_A", "Coverage_Zone_1", "Relay_Node_5", "WiFi_Hub_A"] | (0, 13) | [[0, 2], [0, 5], [0, 6], [0, 9], [0, 10], [0, 12], [1, 5], [1, 7], [1, 9], [2, 5], [2, 10], [4, 6], [4, 12], [5, 7], [5, 9], [5, 11], [6, 7], [6, 8], [7, 8], [7, 9], [7, 11], [8, 9], [11, 12]] | undirected | none | {"Receiver_Station_B": "0", "Network_Node_A": "1", "Access_Point_1": "2", "Receiver_Station_A": "3", "Coverage_Zone_1": "4", "Tower_E": "5", "Access_Point_2": "6", "Signal_Point_B": "7", "Relay_Node_5": "8", "Broadcast_Point_2": "9", "Router_Location_2": "10", "WiFi_Hub_A": "11", "Hotspot_A": "12"} | none | node_list |
real_erdos | dominating_set | wireless_network_coverage | You are designing a wireless network to cover a large area. The network consists of potential tower locations: Mobile_Tower_B, WiFi_Hub_A, Transmitter_1, Antenna_Site_Alpha, Tower_C, Network_Node_B, Network_Node_A, Relay_Node_1, Access_Point_3, Relay_Node_4, Relay_Node_3, WiFi_Hub_B, Base_Station_South, Access_Point_2,... | ["Mobile_Tower_B", "WiFi_Hub_A", "Transmitter_1", "Network_Node_B", "Access_Point_3", "Coverage_Zone_3", "Coverage_Zone_1"] | (0, 20) | [[0, 6], [0, 12], [0, 17], [0, 19], [1, 3], [1, 4], [1, 11], [1, 12], [1, 13], [1, 19], [2, 3], [2, 7], [2, 11], [2, 17], [2, 18], [3, 4], [3, 6], [3, 10], [3, 16], [3, 17], [3, 18], [3, 19], [4, 16], [4, 17], [5, 6], [5, 9], [5, 10], [5, 12], [5, 18], [6, 8], [6, 10], [6, 19], [7, 9], [8, 16], [9, 19], [11, 13], [11, ... | undirected | none | {"Mobile_Tower_B": "0", "WiFi_Hub_A": "1", "Transmitter_1": "2", "Antenna_Site_Alpha": "3", "Tower_C": "4", "Network_Node_B": "5", "Network_Node_A": "6", "Relay_Node_1": "7", "Access_Point_3": "8", "Relay_Node_4": "9", "Relay_Node_3": "10", "WiFi_Hub_B": "11", "Base_Station_South": "12", "Access_Point_2": "13", "Covera... | none | node_list |
real_erdos | dominating_set | wireless_network_coverage | You need to establish wireless coverage for an IoT network. The potential relay nodes are: Tower_B, Access_Point_2, Base_Station_West, Router_Location_1, Hotspot_A, Tower_A, Base_Station_North, Relay_Node_1, Router_Location_2, Coverage_Zone_3, Mobile_Tower_B, Antenna_Site_Beta, Access_Point_3, Wireless_Station_1. The n... | ["Tower_B", "Access_Point_2", "Base_Station_West", "Hotspot_A", "Tower_A", "Mobile_Tower_B"] | (0, 14) | [[0, 9], [0, 11], [1, 3], [1, 9], [1, 12], [2, 3], [2, 6], [2, 7], [2, 8], [2, 13], [3, 4], [3, 8], [5, 11], [5, 12], [8, 11], [8, 12], [9, 12]] | undirected | none | {"Tower_B": "0", "Access_Point_2": "1", "Base_Station_West": "2", "Router_Location_1": "3", "Hotspot_A": "4", "Tower_A": "5", "Base_Station_North": "6", "Relay_Node_1": "7", "Router_Location_2": "8", "Coverage_Zone_3": "9", "Mobile_Tower_B": "10", "Antenna_Site_Beta": "11", "Access_Point_3": "12", "Wireless_Station_1":... | none | node_list |
real_erdos | dominating_set | wireless_network_coverage | You need to establish wireless coverage for an IoT network. The potential relay nodes are: Hotspot_B, Access_Point_5, Tower_B, Tower_D, Hotspot_A, Access_Point_3, Relay_Node_5, Router_Location_1, Tower_F, Signal_Point_A. The network topology is: There is a wireless link between Hotspot_B and Relay_Node_5. Access_Point_... | ["Hotspot_B", "Access_Point_5", "Tower_B", "Tower_D", "Access_Point_3", "Tower_F"] | (0, 10) | [[0, 6], [1, 6], [1, 9], [2, 4], [3, 4], [3, 6], [3, 7], [4, 8], [6, 8], [6, 9]] | undirected | none | {"Hotspot_B": "0", "Access_Point_5": "1", "Tower_B": "2", "Tower_D": "3", "Hotspot_A": "4", "Access_Point_3": "5", "Relay_Node_5": "6", "Router_Location_1": "7", "Tower_F": "8", "Signal_Point_A": "9"} | none | node_list |
real_erdos | dominating_set | wireless_network_coverage | A telecommunications company needs to deploy WiFi access points across a campus. Available locations are: Broadcast_Point_1, Relay_Node_5, Broadcast_Point_2, Receiver_Station_B, Wireless_Station_1, WiFi_Hub_C, Signal_Point_B, Network_Node_A, Antenna_Site_Delta, WiFi_Hub_B, Relay_Node_2, Coverage_Zone_2, WiFi_Hub_A, Hot... | ["Broadcast_Point_1", "Wireless_Station_1", "Network_Node_A", "Hotspot_B", "Tower_B"] | (0, 17) | [[0, 1], [0, 2], [0, 3], [0, 6], [0, 8], [0, 10], [0, 11], [0, 16], [1, 3], [1, 4], [1, 7], [1, 8], [1, 15], [3, 4], [3, 5], [3, 6], [3, 9], [3, 11], [3, 13], [3, 15], [4, 5], [4, 9], [4, 10], [4, 12], [4, 14], [6, 7], [6, 12], [8, 16], [10, 13], [11, 14]] | undirected | none | {"Broadcast_Point_1": "0", "Relay_Node_5": "1", "Broadcast_Point_2": "2", "Receiver_Station_B": "3", "Wireless_Station_1": "4", "WiFi_Hub_C": "5", "Signal_Point_B": "6", "Network_Node_A": "7", "Antenna_Site_Delta": "8", "WiFi_Hub_B": "9", "Relay_Node_2": "10", "Coverage_Zone_2": "11", "WiFi_Hub_A": "12", "Hotspot_B": "... | none | node_list |
real_erdos | dominating_set | wireless_network_coverage | A telecommunications company needs to deploy WiFi access points across a campus. Available locations are: Signal_Point_B, Relay_Node_1, Relay_Node_2, Hotspot_B, Wireless_Station_2, Relay_Node_3, Broadcast_Point_2, Coverage_Zone_2, Base_Station_South, Access_Point_1, Base_Station_East, Transmitter_1, Antenna_Site_Gamma,... | ["Signal_Point_B", "Broadcast_Point_2", "Base_Station_South", "Base_Station_East"] | (0, 16) | [[0, 1], [0, 2], [0, 3], [0, 4], [0, 5], [0, 13], [0, 14], [0, 15], [1, 3], [1, 4], [1, 6], [1, 7], [1, 8], [1, 9], [1, 10], [1, 12], [2, 5], [5, 6], [6, 7], [6, 11], [6, 12], [7, 8], [8, 9], [8, 11], [8, 14], [8, 15], [9, 10], [9, 13]] | undirected | none | {"Signal_Point_B": "0", "Relay_Node_1": "1", "Relay_Node_2": "2", "Hotspot_B": "3", "Wireless_Station_2": "4", "Relay_Node_3": "5", "Broadcast_Point_2": "6", "Coverage_Zone_2": "7", "Base_Station_South": "8", "Access_Point_1": "9", "Base_Station_East": "10", "Transmitter_1": "11", "Antenna_Site_Gamma": "12", "WiFi_Hub_... | none | node_list |
real_erdos | dominating_set | wireless_network_coverage | A telecommunications company needs to deploy WiFi access points across a campus. Available locations are: Signal_Point_B, Broadcast_Point_1, Tower_D, Tower_B, Receiver_Station_A, Access_Point_1, Signal_Point_A, Tower_F, Tower_G, WiFi_Hub_B, Mobile_Tower_A, Router_Location_2. Each access point covers its own location an... | ["Signal_Point_B", "Broadcast_Point_1", "Tower_D", "Tower_B", "Tower_G", "Router_Location_2"] | (0, 12) | [[1, 4], [1, 7], [1, 10], [2, 5], [2, 9], [3, 6], [4, 7], [5, 8], [5, 9], [6, 9], [6, 10], [6, 11], [7, 10], [7, 11]] | undirected | none | {"Signal_Point_B": "0", "Broadcast_Point_1": "1", "Tower_D": "2", "Tower_B": "3", "Receiver_Station_A": "4", "Access_Point_1": "5", "Signal_Point_A": "6", "Tower_F": "7", "Tower_G": "8", "WiFi_Hub_B": "9", "Mobile_Tower_A": "10", "Router_Location_2": "11"} | none | node_list |
real_erdos | dominating_set | wireless_network_coverage | You need to establish wireless coverage for an IoT network. The potential relay nodes are: Access_Point_3, Coverage_Zone_2, Antenna_Site_Gamma, WiFi_Hub_C, Network_Node_A, Access_Point_1, Access_Point_4, WiFi_Hub_B, Relay_Node_4, Tower_E, Access_Point_2, Hotspot_A, Relay_Node_1, Cell_Tower_1, Broadcast_Point_1, Coverag... | ["Access_Point_3", "WiFi_Hub_C", "Relay_Node_4", "Hotspot_A"] | (0, 18) | [[0, 1], [0, 2], [0, 4], [0, 6], [0, 7], [0, 9], [0, 10], [0, 12], [0, 13], [1, 4], [1, 9], [1, 13], [2, 3], [2, 5], [2, 7], [2, 13], [2, 14], [2, 15], [3, 5], [3, 9], [3, 12], [3, 13], [3, 16], [3, 17], [4, 8], [4, 9], [4, 10], [4, 11], [4, 12], [4, 13], [4, 14], [4, 16], [5, 14], [5, 15], [6, 10], [6, 16], [7, 17], [... | undirected | none | {"Access_Point_3": "0", "Coverage_Zone_2": "1", "Antenna_Site_Gamma": "2", "WiFi_Hub_C": "3", "Network_Node_A": "4", "Access_Point_1": "5", "Access_Point_4": "6", "WiFi_Hub_B": "7", "Relay_Node_4": "8", "Tower_E": "9", "Access_Point_2": "10", "Hotspot_A": "11", "Relay_Node_1": "12", "Cell_Tower_1": "13", "Broadcast_Poi... | none | node_list |
real_erdos | dominating_set | wireless_network_coverage | You need to establish wireless coverage for an IoT network. The potential relay nodes are: Network_Node_A, Router_Location_2, Relay_Node_4, Transmitter_2, Tower_D, Base_Station_West, Broadcast_Point_2, Tower_H, Antenna_Site_Beta, Base_Station_North, Cell_Tower_2. The network topology is: Network_Node_A has line-of-sigh... | ["Network_Node_A", "Relay_Node_4", "Transmitter_2", "Tower_H", "Base_Station_North"] | (0, 11) | [[0, 1], [0, 4], [0, 5], [1, 4], [2, 8], [3, 6], [4, 5], [4, 10], [5, 7], [6, 7], [8, 10], [9, 10]] | undirected | none | {"Network_Node_A": "0", "Router_Location_2": "1", "Relay_Node_4": "2", "Transmitter_2": "3", "Tower_D": "4", "Base_Station_West": "5", "Broadcast_Point_2": "6", "Tower_H": "7", "Antenna_Site_Beta": "8", "Base_Station_North": "9", "Cell_Tower_2": "10"} | none | node_list |
real_erdos | dominating_set | wireless_network_coverage | We're optimizing a cellular network deployment. The candidate cell tower sites are: Tower_C, WiFi_Hub_C, Coverage_Zone_3, Coverage_Zone_1, Access_Point_2, Base_Station_East, Tower_E, Tower_H, Base_Station_South, Transmitter_1, Access_Point_1, Access_Point_4, Wireless_Station_1, WiFi_Hub_B, Base_Station_West, with the f... | ["Tower_C", "WiFi_Hub_C", "Coverage_Zone_3", "Coverage_Zone_1"] | (0, 15) | [[0, 4], [0, 5], [0, 9], [0, 10], [0, 13], [1, 6], [1, 7], [1, 8], [1, 12], [1, 14], [2, 5], [2, 8], [2, 11], [2, 13], [2, 14], [3, 6], [3, 9], [3, 10], [4, 10], [4, 12], [5, 13], [5, 14], [6, 13], [6, 14], [7, 10], [8, 9], [8, 14], [9, 14], [10, 11], [10, 12], [12, 13], [13, 14]] | undirected | none | {"Tower_C": "0", "WiFi_Hub_C": "1", "Coverage_Zone_3": "2", "Coverage_Zone_1": "3", "Access_Point_2": "4", "Base_Station_East": "5", "Tower_E": "6", "Tower_H": "7", "Base_Station_South": "8", "Transmitter_1": "9", "Access_Point_1": "10", "Access_Point_4": "11", "Wireless_Station_1": "12", "WiFi_Hub_B": "13", "Base_Stat... | none | node_list |
real_erdos | dominating_set | wireless_network_coverage | A telecommunications company needs to deploy WiFi access points across a campus. Available locations are: Cell_Tower_1, Tower_G, Wireless_Station_1, Tower_A, Base_Station_South, Antenna_Site_Delta, Relay_Node_4, Hotspot_B, Base_Station_North, Network_Node_B, Network_Node_A, Tower_H, Access_Point_3, Hotspot_A, Coverage_... | ["Cell_Tower_1", "Antenna_Site_Delta", "Base_Station_North", "Tower_H", "Hotspot_A", "Coverage_Zone_1", "Transmitter_1"] | (0, 16) | [[0, 1], [0, 2], [0, 3], [0, 4], [0, 6], [0, 7], [2, 3], [2, 5], [2, 8], [2, 10], [3, 4], [3, 5], [3, 6], [4, 11], [4, 12], [4, 15], [5, 9], [6, 7], [6, 13], [6, 14], [6, 15], [7, 8], [7, 9], [8, 10], [8, 12], [9, 11], [10, 13], [10, 14]] | undirected | none | {"Cell_Tower_1": "0", "Tower_G": "1", "Wireless_Station_1": "2", "Tower_A": "3", "Base_Station_South": "4", "Antenna_Site_Delta": "5", "Relay_Node_4": "6", "Hotspot_B": "7", "Base_Station_North": "8", "Network_Node_B": "9", "Network_Node_A": "10", "Tower_H": "11", "Access_Point_3": "12", "Hotspot_A": "13", "Coverage_Zo... | none | node_list |
real_erdos | dominating_set | wireless_network_coverage | You need to establish wireless coverage for an IoT network. The potential relay nodes are: Transmitter_2, Base_Station_East, Access_Point_2, Tower_C, Wireless_Station_2, Tower_D, Antenna_Site_Delta, Access_Point_4, Access_Point_5, Access_Point_3, Network_Node_A, Transmitter_1, Relay_Node_1, Antenna_Site_Beta, Tower_E, ... | ["Transmitter_2", "Base_Station_East", "Wireless_Station_2", "Access_Point_5", "Network_Node_A", "Tower_E"] | (0, 17) | [[0, 2], [0, 3], [0, 6], [0, 12], [0, 13], [1, 3], [1, 5], [1, 6], [1, 7], [1, 12], [2, 5], [2, 6], [2, 8], [2, 9], [2, 12], [2, 13], [2, 16], [3, 5], [3, 7], [3, 8], [3, 9], [3, 14], [3, 16], [4, 5], [4, 9], [4, 11], [5, 8], [5, 11], [5, 15], [5, 16], [6, 7], [6, 9], [6, 11], [6, 13], [6, 14], [6, 15], [6, 16], [7, 11... | undirected | none | {"Transmitter_2": "0", "Base_Station_East": "1", "Access_Point_2": "2", "Tower_C": "3", "Wireless_Station_2": "4", "Tower_D": "5", "Antenna_Site_Delta": "6", "Access_Point_4": "7", "Access_Point_5": "8", "Access_Point_3": "9", "Network_Node_A": "10", "Transmitter_1": "11", "Relay_Node_1": "12", "Antenna_Site_Beta": "13... | none | node_list |
real_erdos | dominating_set | wireless_network_coverage | We're optimizing a cellular network deployment. The candidate cell tower sites are: Receiver_Station_A, Tower_E, Antenna_Site_Alpha, Antenna_Site_Delta, Wireless_Station_2, Base_Station_North, Hotspot_A, Tower_H, Tower_B, Base_Station_West, Relay_Node_3, Access_Point_3, Antenna_Site_Gamma, Wireless_Station_1, Receiver_... | ["Receiver_Station_A", "Tower_E", "Antenna_Site_Alpha", "Antenna_Site_Delta", "Base_Station_North", "Hotspot_A"] | (0, 16) | [[0, 4], [0, 11], [0, 12], [0, 13], [1, 4], [1, 9], [1, 12], [1, 13], [1, 14], [2, 9], [2, 14], [2, 15], [3, 7], [3, 13], [4, 11], [5, 7], [5, 10], [5, 12], [5, 14], [5, 15], [6, 8], [6, 10], [6, 12], [6, 14], [8, 11], [8, 12], [9, 11], [10, 11], [11, 12], [12, 13]] | undirected | none | {"Receiver_Station_A": "0", "Tower_E": "1", "Antenna_Site_Alpha": "2", "Antenna_Site_Delta": "3", "Wireless_Station_2": "4", "Base_Station_North": "5", "Hotspot_A": "6", "Tower_H": "7", "Tower_B": "8", "Base_Station_West": "9", "Relay_Node_3": "10", "Access_Point_3": "11", "Antenna_Site_Gamma": "12", "Wireless_Station_... | none | node_list |
real_erdos | dominating_set | wireless_network_coverage | You are designing a wireless network to cover a large area. The network consists of potential tower locations: Hotspot_A, Transmitter_2, Hotspot_B, Base_Station_West, Network_Node_B, Relay_Node_5, Receiver_Station_B, Access_Point_4, Antenna_Site_Gamma, Coverage_Zone_1, Relay_Node_3, Antenna_Site_Delta, Broadcast_Point_... | ["Hotspot_A", "Access_Point_4", "Coverage_Zone_1", "Coverage_Zone_3"] | (0, 19) | [[0, 1], [0, 2], [0, 3], [0, 4], [0, 5], [0, 6], [0, 8], [0, 11], [0, 13], [0, 17], [1, 4], [1, 5], [1, 6], [1, 7], [1, 9], [1, 10], [1, 15], [1, 16], [1, 18], [2, 7], [3, 4], [3, 5], [3, 6], [3, 8], [3, 9], [4, 8], [4, 11], [4, 18], [6, 7], [6, 9], [6, 12], [6, 13], [6, 14], [6, 15], [7, 12], [8, 10], [8, 11], [8, 13]... | undirected | none | {"Hotspot_A": "0", "Transmitter_2": "1", "Hotspot_B": "2", "Base_Station_West": "3", "Network_Node_B": "4", "Relay_Node_5": "5", "Receiver_Station_B": "6", "Access_Point_4": "7", "Antenna_Site_Gamma": "8", "Coverage_Zone_1": "9", "Relay_Node_3": "10", "Antenna_Site_Delta": "11", "Broadcast_Point_1": "12", "Tower_G": "1... | none | node_list |
real_erdos | dominating_set | wireless_network_coverage | You are designing a wireless network to cover a large area. The network consists of potential tower locations: Relay_Node_3, Base_Station_West, Antenna_Site_Alpha, Cell_Tower_1, Mobile_Tower_B, Tower_A, Transmitter_1, Coverage_Zone_1, Access_Point_3, Network_Node_B, Hotspot_B, Receiver_Station_B, Antenna_Site_Delta, Ho... | ["Relay_Node_3", "Cell_Tower_1", "Coverage_Zone_1", "Access_Point_3", "Network_Node_B", "Hotspot_B"] | (0, 15) | [[0, 1], [0, 2], [0, 5], [1, 3], [1, 6], [1, 7], [1, 8], [1, 10], [1, 11], [1, 12], [2, 3], [2, 4], [3, 4], [3, 6], [3, 11], [3, 14], [4, 5], [4, 8], [5, 9], [5, 10], [6, 7], [6, 9], [6, 14], [8, 13], [9, 12], [9, 13]] | undirected | none | {"Relay_Node_3": "0", "Base_Station_West": "1", "Antenna_Site_Alpha": "2", "Cell_Tower_1": "3", "Mobile_Tower_B": "4", "Tower_A": "5", "Transmitter_1": "6", "Coverage_Zone_1": "7", "Access_Point_3": "8", "Network_Node_B": "9", "Hotspot_B": "10", "Receiver_Station_B": "11", "Antenna_Site_Delta": "12", "Hotspot_A": "13",... | none | node_list |
real_erdos | dominating_set | wireless_network_coverage | You need to establish wireless coverage for an IoT network. The potential relay nodes are: Access_Point_1, Coverage_Zone_1, Tower_E, Signal_Point_A, Base_Station_West, WiFi_Hub_C, Tower_C, Tower_F, WiFi_Hub_B, Tower_D, WiFi_Hub_A, Receiver_Station_B, Hotspot_A, Tower_B, Coverage_Zone_2. The network topology is: Access_... | ["Access_Point_1", "WiFi_Hub_C", "WiFi_Hub_B", "Tower_D", "Receiver_Station_B", "Hotspot_A"] | (0, 15) | [[0, 1], [0, 2], [0, 3], [0, 4], [0, 7], [0, 14], [2, 3], [2, 4], [2, 5], [2, 6], [2, 7], [2, 8], [2, 9], [3, 9], [4, 5], [5, 6], [5, 10], [6, 10], [6, 11], [7, 8], [7, 12], [9, 14], [10, 11], [10, 12], [10, 13], [11, 13]] | undirected | none | {"Access_Point_1": "0", "Coverage_Zone_1": "1", "Tower_E": "2", "Signal_Point_A": "3", "Base_Station_West": "4", "WiFi_Hub_C": "5", "Tower_C": "6", "Tower_F": "7", "WiFi_Hub_B": "8", "Tower_D": "9", "WiFi_Hub_A": "10", "Receiver_Station_B": "11", "Hotspot_A": "12", "Tower_B": "13", "Coverage_Zone_2": "14"} | none | node_list |
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