Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4651389 | Discrete Mathematics | 2006 | 9 Pages |
Abstract
In this paper, we study the problem of sampling (exactly) uniformly from the set of linear extensions of an arbitrary partial order. Previous Markov chain techniques have yielded algorithms that generate approximately uniform samples. Here, we create a bounding chain for one such Markov chain, and by using a non-Markovian coupling together with a modified form of coupling from the past, we build an algorithm for perfectly generating samples. The expected running time of the procedure is O(n3lnn)O(n3lnn), making the technique as fast as the mixing time of the Karzanov/Khachiyan chain upon which it is based.
Related Topics
Physical Sciences and Engineering
Mathematics
Discrete Mathematics and Combinatorics
Authors
Mark Huber,