Generating a Random Linear Extension of a Partial Order
Peter Matthews · The Annals of Probability · 1991
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.