| import OAI.Combinatorics.ContingencyTables.Sampling.AllSamplingMachine |
| import OAI.Combinatorics.ContingencyTables.Sampling.ExactSamplingMachine |
| import OAI.Combinatorics.ContingencyTables.Counting.CountingMainMachine |
| import OAI.Combinatorics.ContingencyTables.Dense.FiniteBoxPrekopa |
| import OAI.Combinatorics.ContingencyTables.Dense.FiniteCheegerProof |
| import OAI.Combinatorics.ContingencyTables.Transport.EdmondsKarpBound |
|
|
| namespace OAI |
|
|
| /-! # Sampling and counting contingency tables with arbitrary margins |
|
|
| The finite-box Prékopa–Leindler inequality, finite Cheeger inequality |
| and Edmonds–Karp bound yield sampling and counting algorithms with |
| uniform polynomial bit-cost guarantees. |
| -/ |
| namespace ContingencyTables |
|
|
| /-- Paper 200-01: an almost-uniform sampler with polynomial cost on every execution. -/ |
| theorem boundedSampling : Algorithms.BoundedSamplingStatement := |
| SmallGraphProfiles.boundedSampling_conditional |
| PublishedInputs.finiteBoxPrekopaLeindler (fun _ _ => CheegerProof.finiteCheeger) |
|
|
| /-- Paper 200-01: exact uniform sampling in expected polynomial bit time. -/ |
| theorem exactSampling : Algorithms.ExactSamplingStatement := |
| SmallGraphProfiles.exactSampling_conditional |
| PublishedInputs.finiteBoxPrekopaLeindler (fun _ _ => CheegerProof.finiteCheeger) |
|
|
| /-- Paper 200-02: the cell-bounded counting FPRAS with a public fair-bit machine. -/ |
| theorem counting : Algorithms.CountingStatement := |
| CountingExecutedMachine.counting_conditional EdmondsKarpBound.edmondsKarp1972Theorem1 |
| PublishedInputs.finiteBoxPrekopaLeindler (fun _ _ => CheegerProof.finiteCheeger) |
|
|
| end ContingencyTables |
|
|
| end OAI |
|
|
