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e5a97c6 | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 | import Mathlib
import OAI.Combinatorics.MatchingCount.Sampling.ChosenChord
namespace OAI
namespace MatchingFPRAS.Transport.CellDemands
variable {V L : Type*} [Fintype V] [DecidableEq V] [Fintype L] [DecidableEq L]
variable {bags : V → Finset L} {G : SimpleGraph L}
noncomputable local instance finiteSampler3WeightedCellBagEdgeFintype : Fintype (BagEdge bags) := Fintype.ofFinite _
variable {hbags : ∀ v, ∀ a ∈ bags v, ∀ b ∈ bags v, a = b ∨ G.Adj a b}
variable {hG : G.IsAcyclic}
variable (height : L → ℝ) (hheight : ∀ l, 0 < height l)
variable (hstep : ∀ a b, G.Adj a b → height a ≤ 2 * height b)
variable (D : ℝ) (hD : 1 ≤ D) (w : BagEdge bags → ℝ)
variable (hw : ∀ e, height e.color / D ≤ w e ∧ w e ≤ 3 * height e.color)
variable (lo hi : ℝ) (hlo : 0 < lo) (hlohi : lo ≤ hi)
include hheight hstep hD hw hlohi
variable {V L : Type*} [Fintype V] [DecidableEq V] [Fintype L] [DecidableEq L]
variable {bags : V → Finset L} {G : SimpleGraph L}
noncomputable local instance finiteSampler3AcyclicCellBagEdgeFintype : Fintype (BagEdge bags) := Fintype.ofFinite _
variable {hbags : ∀ v, ∀ a ∈ bags v, ∀ b ∈ bags v, a = b ∨ G.Adj a b}
variable {hG : G.IsAcyclic}
variable {V L : Type*} [Fintype V] [DecidableEq V] [Fintype L] [DecidableEq L]
variable {bags : V → Finset L} {G : SimpleGraph L}
noncomputable local instance finiteSampler3DemandCellBagEdgeFintype : Fintype (BagEdge bags) := Fintype.ofFinite _
variable {hbags : ∀ v, ∀ a ∈ bags v, ∀ b ∈ bags v, a = b ∨ G.Adj a b}
variable {hG : G.IsAcyclic}
end MatchingFPRAS.Transport.CellDemands
namespace MatchingFPRAS.Transport
variable {V L : Type*} [Fintype V] [DecidableEq V] [Fintype L] [DecidableEq L]
variable {bags : V → Finset L} {G : SimpleGraph L}
noncomputable local instance finiteSampler3TransportBagEdgeFintype : Fintype (BagEdge bags) := Fintype.ofFinite _
variable (hbags : ∀ v, ∀ a ∈ bags v, ∀ b ∈ bags v, a = b ∨ G.Adj a b)
variable (hG : G.IsAcyclic)
end MatchingFPRAS.Transport
namespace MatchingFPRAS.Transport.CellDemands
variable {V L : Type*} [Fintype V] [DecidableEq V] [Fintype L] [DecidableEq L]
variable {bags : V → Finset L} {G : SimpleGraph L}
noncomputable local instance finiteSampler3BoundedCellBagEdgeFintype : Fintype (BagEdge bags) := Fintype.ofFinite _
variable {hbags : ∀ v, ∀ a ∈ bags v, ∀ b ∈ bags v, a = b ∨ G.Adj a b}
variable {hG : G.IsAcyclic}
variable (height : L → ℝ) (hheight : ∀ l, 0 < height l)
variable (hstep : ∀ a b, G.Adj a b → height a ≤ 2 * height b)
variable (D : ℝ) (hD : 1 ≤ D) (w : BagEdge bags → ℝ)
variable (hw : ∀ e, height e.color / D ≤ w e ∧ w e ≤ 3 * height e.color)
variable (lo hi : ℝ) (hlo : 0 < lo) (hlohi : lo ≤ hi)
include hheight hstep hD hw hlo hlohi hbags hG
end MatchingFPRAS.Transport.CellDemands
namespace MatchingFPRAS.Transport
open Finset
variable {V L : Type*} [Fintype V] [DecidableEq V] [Fintype L] [DecidableEq L]
variable {bags : V → Finset L}
noncomputable local instance finiteSampler3BagEdgeFintype : Fintype (BagEdge bags) := Fintype.ofFinite _
end MatchingFPRAS.Transport
end OAI
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