OpenAI reports exact uniform sampling of contingency tables with arbitrary margins

For any nonnegative row and column margins with equal totals, an exact uniform sampler for integer contingency tables terminates almost surely and has expected bit complexity polynomial in both dimensions and the binary input length.

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Understanding the problem

Read the background

For any nonnegative row and column margins with equal totals, an exact uniform sampler for integer contingency tables terminates almost surely and has expected bit complexity polynomial in both dimensions and the binary input length.

Why it matters

If correct, gives exact uniform sampling with no structural restriction on the margins or dimensions.

What counts as progress

Can contingency tables with arbitrary prescribed margins be sampled exactly uniformly in expected polynomial bit time?

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