| import Mathlib |
| import OAI.Combinatorics.MatchingCount.Algorithm.OnlineRequest |
| import OAI.Combinatorics.MatchingCount.Algorithm.OnlineTransitionLaw |
|
|
| namespace OAI |
|
|
| namespace MatchingFPRAS.OnlineSchedule |
| open PhysicalStream TreeTyped TreeFraction ExecutableSource ExecutableScaling Transport |
| open UnitRefresh Enlargement TreeTyped.Numbered OnlineStage ExecutableRefresh |
|
|
| attribute [local instance] NumberedHierarchy.labelOrder |
| attribute [local instance] Transport.sym2Order Transport.bagEdgeOrder Transport.bagEdgeFintype |
| attribute [local instance] UnitRefresh.Computable.allowedDec Transport.prodOrder Transport.sumOrder |
|
|
| lemma bitPrecision_inverseNat (R m : ℕ) : bitPrecision R (1/(m:ℚ))=Nat.clog 2 (R*m) := by |
| simp [bitPrecision] |
|
|
| variable {G : GraphInput} [Nontrivial (Fin G.n)] |
| lemma sourceRequest_source {j : ℕ} (p : Trial.Parameters G) (s : FiniteTrial.ScaleState G j) : |
| sourceRequest (fixedData p s,p.S)=fixedRequest p s := by |
| unfold sourceRequest |
| rw [show sourcePrecision (fixedData p s,p.S)= |
| (((((Fintype.card (SourceVertex (Fin G.n) p.K)),FiniteTrial.sourceD (G:=G) p.K), |
| (p.K,tierCount (n:=G.n) p.K (FiniteTrial.sourceD (G:=G) p.K))),denominator p), |
| (edgeCount s.activity p.K,labelCount s.activity p.K)) from by |
| simpa only [fixedData,denominator,edgeCount,labelCount,List.length_replicate] using |
| sourcePrecision_source p.hn s p.K (FiniteTrial.sourceD (G:=G) p.K) p.S |
| (List.replicate (tierCount (n:=G.n) p.K (FiniteTrial.sourceD (G:=G) p.K)) false) |
| (List.replicate (copies (n:=G.n) p.K (FiniteTrial.sourceD (G:=G) p.K)) false)] |
| have hc : (sourceTables (sparseBagInput (fixedData p s))).1.length=edgeCount s.activity p.K := by |
| unfold fixedData |
| rw [sparseBagInput_source,sourceTables_catalog p.hn s.activity |
| (fun i j=>(s.activity_pos i j).le) p.K] |
| simp only [sourceCatalog,List.length_ofFn] |
| simp only [hc,precisionPlan,fixedRequest,choiceWidth,markWidth,bitPrecision_inverseNat] |
| apply Prod.ext |
| · rfl |
| · apply Prod.ext |
| · rfl |
| · simp only [index_orderedEnum] |
| apply List.ext_getElem |
| · simp |
| · intro _ _ _ |
| simp |
| end MatchingFPRAS.OnlineSchedule |
|
|
| end OAI |
|
|
