Generating a random sinkfree orientation in quadratic time
Abstract
A sinkfree orientation of a finite undirected graph is a choice of orientation for each edge such that every vertex has outdegree at least 1. Bubley and Dyer (1997) use Markov Chain Monte Carlo to sample approximately from the uniform distribution on sinkfree orientations in time O(m^3 log (1/epsilon)), where m is the number of edges and epsilon the degree of approximation. Huber (1998) uses coupling from the past to obtain an exact sample in time O(m^4). We present a simple randomized algorithm inspired by Wilson's cycle popping method which obtains an exact sample in mean time at most O(nm), where n is the number of vertices.
 Publication:

arXiv Mathematics eprints
 Pub Date:
 March 2001
 arXiv:
 arXiv:math/0103189
 Bibcode:
 2001math......3189C
 Keywords:

 Mathematics  Probability;
 Mathematics  Combinatorics
 EPrint:
 13 pages