Generating a random sink-free orientation in quadratic time
Abstract
A sink-free orientation of a finite undirected graph is a choice of orientation for each edge such that every vertex has out-degree at least 1. Bubley and Dyer (1997) use Markov Chain Monte Carlo to sample approximately from the uniform distribution on sink-free 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:
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arXiv Mathematics e-prints
- Pub Date:
- March 2001
- DOI:
- 10.48550/arXiv.math/0103189
- arXiv:
- arXiv:math/0103189
- Bibcode:
- 2001math......3189C
- Keywords:
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- Mathematics - Probability;
- Mathematics - Combinatorics
- E-Print:
- 13 pages