Abstract
Given a partial order of $N$ items, a linear extension that is almost uniformly distributed, in the sense of variation distance, is generated. The algorithm runs in polynomial time. The technique used is a coupling for a random walk on a polygonal subset of the unit sphere in $\mathbb{R}^N$. Including is a discussion of how accurately the steps of the random walk must be computed.
Citation
Peter Matthews. "Generating a Random Linear Extension of a Partial Order." Ann. Probab. 19 (3) 1367 - 1392, July, 1991. https://doi.org/10.1214/aop/1176990349
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