| import Mathlib |
| import OAI.Combinatorics.MatchingCount.Sampling.PM |
| import OAI.Combinatorics.MatchingCount.Graphs.Density |
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| namespace OAI |
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| namespace MatchingFPRAS.Transport |
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| open Finset MatchingFPRAS.Replica |
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| variable {V L : Type*} [Fintype V] [DecidableEq V] [Fintype L] [DecidableEq L] |
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| variable {bags : V → Finset L} {G : SimpleGraph L} |
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| noncomputable local instance finiteSampler4BagEdgeFintype : Fintype (BagEdge bags) := Fintype.ofFinite _ |
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| variable (hbags : ∀ v, ∀ a ∈ bags v, ∀ b ∈ bags v, a = b ∨ G.Adj a b) |
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| variable (hG : G.IsAcyclic) |
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| open Finset MatchingFPRAS.Replica |
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| variable {V L : Type*} [Fintype V] [DecidableEq V] [Fintype L] [DecidableEq L] |
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| variable {bags : V → Finset L} {G : SimpleGraph L} |
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| noncomputable local instance finiteSampler4BagEdgeFintype2 : Fintype (BagEdge bags) := Fintype.ofFinite _ |
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| variable {hbags : ∀ v, ∀ a ∈ bags v, ∀ b ∈ bags v, a = b ∨ G.Adj a b} |
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| variable {hG : G.IsAcyclic} |
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| variable (height : L → ℝ) (hheight : ∀ l, 0 < height l) |
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| variable (hstep : ∀ a b, G.Adj a b → height a ≤ 2 * height b) |
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| variable (D : ℝ) (hD : 1 ≤ D) (w : BagEdge bags → ℝ) |
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| variable (hw : ∀ e, height e.color / D ≤ w e ∧ w e ≤ 3 * height e.color) |
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| include hheight hstep hD hw hbags hG |
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| open Finset MatchingFPRAS.Replica |
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| variable {V L : Type*} [Fintype V] [DecidableEq V] [Fintype L] [DecidableEq L] |
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| variable {bags : V → Finset L} {G : SimpleGraph L} |
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| noncomputable local instance finiteSampler4BagEdgeFintype3 : Fintype (BagEdge bags) := Fintype.ofFinite _ |
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| variable {hbags : ∀ v, ∀ a ∈ bags v, ∀ b ∈ bags v, a = b ∨ G.Adj a b} |
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| variable {hG : G.IsAcyclic} |
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| variable (height : L → ℝ) (hheight : ∀ l, 0 < height l) |
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| variable (hstep : ∀ a b, G.Adj a b → height a ≤ 2 * height b) |
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| variable (D : ℝ) (hD : 1 ≤ D) (w : BagEdge bags → ℝ) |
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| variable (hw : ∀ e, height e.color / D ≤ w e ∧ w e ≤ 3 * height e.color) |
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| include hheight hstep hD hw hbags hG |
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| open Finset MatchingFPRAS.Replica |
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| variable {V J : Type*} [Fintype V] [DecidableEq V] [Fintype J] [DecidableEq J] |
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| variable {bags : V → Finset J} {G : SimpleGraph J} |
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| noncomputable local instance finiteSampler4BagEdgeFintype4 : Fintype (BagEdge bags) := Fintype.ofFinite _ |
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| variable (hbags : ∀ v, ∀ a ∈ bags v, ∀ b ∈ bags v, a = b ∨ G.Adj a b) |
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| variable (hG : G.IsAcyclic) |
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| open Finset MatchingFPRAS.Replica |
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| variable {V J : Type*} [Fintype V] [DecidableEq V] [Fintype J] [DecidableEq J] |
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| variable {bags : V → Finset J} {G : SimpleGraph J} |
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| noncomputable local instance finiteSampler4BagEdgeFintype5 : Fintype (BagEdge bags) := Fintype.ofFinite _ |
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| variable {hbags : ∀ v, ∀ a ∈ bags v, ∀ b ∈ bags v, a = b ∨ G.Adj a b} |
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| variable {hG : G.IsAcyclic} |
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| variable (height : J → ℝ) (hheight : ∀ l, 0 < height l) |
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| variable (hstep : ∀ a b, G.Adj a b → height a ≤ 2 * height b) |
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| variable (D : ℕ) (hD : 1 ≤ D) (w : BagEdge bags → ℝ) |
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| variable (hw : ∀ e, height e.color / D ≤ w e ∧ w e ≤ 3 * height e.color) |
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| include hheight hstep hD hw hbags hG |
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| open Finset MatchingFPRAS.Replica |
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| variable {V J : Type*} [Fintype V] [DecidableEq V] [Fintype J] [DecidableEq J] |
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| variable {bags : V → Finset J} {G : SimpleGraph J} |
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| noncomputable local instance finiteSampler4BagEdgeFintype6 : Fintype (BagEdge bags) := Fintype.ofFinite _ |
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| noncomputable local instance finiteSampler4PMDecidableEq : DecidableEq (PM (BagEdge.Incident (bags := bags))) := Classical.decEq _ |
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| open Finset MatchingFPRAS.Replica |
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| variable {V J : Type*} [Fintype V] [DecidableEq V] [Fintype J] [DecidableEq J] |
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| variable {bags : V → Finset J} {G : SimpleGraph J} |
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| noncomputable local instance finiteSampler4BagEdgeFintype7 : Fintype (BagEdge bags) := Fintype.ofFinite _ |
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| noncomputable local instance finiteSampler4WeightedPMDecidableEq : DecidableEq (PM (BagEdge.Incident (bags := bags))) := Classical.decEq _ |
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| variable {hbags : ∀ v, ∀ a ∈ bags v, ∀ b ∈ bags v, a = b ∨ G.Adj a b} |
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| variable {hG : G.IsAcyclic} |
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| variable (height : J → ℝ) (hheight : ∀ l, 0 < height l) |
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| variable (hstep : ∀ a b, G.Adj a b → height a ≤ 2 * height b) |
|
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| variable (D : ℕ) (hD : 1 ≤ D) (w : BagEdge bags → ℝ) |
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| variable (hw : ∀ e, height e.color / D ≤ w e ∧ w e ≤ 3 * height e.color) |
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| include hheight hstep hD hw hbags hG |
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| open Finset MatchingFPRAS.Replica |
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| variable {V J : Type*} [Fintype V] [DecidableEq V] [Fintype J] [DecidableEq J] |
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| variable {bags : V → Finset J} {G : SimpleGraph J} |
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| noncomputable local instance finiteSampler4BagEdgeFintype8 : Fintype (BagEdge bags) := Fintype.ofFinite _ |
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| open Finset MatchingFPRAS.Replica |
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| variable {V J : Type*} [Fintype V] [DecidableEq V] [Fintype J] [DecidableEq J] |
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| variable {bags : V → Finset J} {G : SimpleGraph J} |
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| noncomputable local instance finiteSampler4BagEdgeFintype9 : Fintype (BagEdge bags) := Fintype.ofFinite _ |
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| open Finset MatchingFPRAS.Replica |
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| variable {V J : Type*} [Fintype V] [DecidableEq V] [Fintype J] [DecidableEq J] |
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| variable {bags : V → Finset J} {G : SimpleGraph J} |
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| noncomputable local instance finiteSampler4BagEdgeFintype10 : Fintype (BagEdge bags) := Fintype.ofFinite _ |
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| end MatchingFPRAS.Transport |
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| end OAI |
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|
