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d5b7741 | 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 | 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
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