| import Mathlib |
| import OAI.Combinatorics.MatchingCount.Graphs.Cycle |
|
|
| namespace OAI |
|
|
| namespace MatchingFPRAS.Transport |
|
|
| variable {V E : Type*} [Fintype V] [DecidableEq V] [Fintype E] [DecidableEq E] |
|
|
| variable {inc : E → V → Prop} |
|
|
| namespace LongComponent |
|
|
| variable {p : PM inc × PM inc} (S : LongComponent p) |
|
|
| noncomputable instance : Fintype (LongComponent p) := Fintype.ofFinite _ |
|
|
| end LongComponent |
|
|
| end MatchingFPRAS.Transport |
|
|
| namespace MatchingFPRAS.Transport.CellDemands |
|
|
| variable {V L : Type*} [Fintype V] [DecidableEq V] [Fintype L] [DecidableEq L] |
|
|
| variable {bags : V → Finset L} |
|
|
| noncomputable local instance finiteSampler2BagEdgeFintype : Fintype (BagEdge bags) := Fintype.ofFinite _ |
|
|
| variable {G : SimpleGraph L} |
|
|
| 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 finiteSampler2DemandBagEdgeFintype : Fintype (BagEdge bags) := Fintype.ofFinite _ |
|
|
| variable {hbags : ∀ v, ∀ a ∈ bags v, ∀ b ∈ bags v, a = b ∨ G.Adj a b} |
|
|
| variable {hG : G.IsAcyclic} |
|
|
| noncomputable instance : Fintype (Demand hbags hG) := Fintype.ofFinite _ |
|
|
| noncomputable instance : Fintype (ErrorDemand hbags hG) := Fintype.ofFinite _ |
|
|
| 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) |
|
|
| end MatchingFPRAS.Transport.CellDemands |
|
|
| namespace MatchingFPRAS.Transport |
|
|
| variable {V E : Type*} [Fintype V] [DecidableEq V] [DecidableEq E] |
|
|
| variable {inc : E → V → Prop} |
|
|
| namespace PatternCode |
|
|
| variable (x : PatternCode inc) |
|
|
| variable [Fintype E] |
|
|
| noncomputable instance finiteSampler2PatternCodeFintype : Fintype (PatternCode inc) := Fintype.ofFinite _ |
|
|
| end PatternCode |
|
|
| 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 finiteSampler2AcyclicBagEdgeFintype : 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 finiteSampler2CellBagEdgeFintype : 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 finiteSampler2ErrorBagEdgeFintype : 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 |
|
|
| end OAI |
|
|
