Random Bichromatic Matchings

Given a graph with edges colored Red and Blue, we wish to sample and approximately count the number of perfect matchings with exactly k Red edges. We study a Markov chain on the space of all matchings of a graph that favors matchings with k Red edges. We show that it is rapidly mixing using non-traditional canonical paths that can backtrack, based on an algorithm for a simple combinatorial problem. We show that this chain can be used to sample dimer configurations on a 2-dimensional toroidal region with k Red edges.

• Type: Journal
• Year: 2008
• Where: ALGORITHMICA
• Authors: Nayantara Bhatnagar, Dana Randall, Vijay V. Vazirani, Eric Vigoda
• Keywords: ALGORITHMICA 2008, Non-traditional Canonical Paths, Perfect Matchings, Simple Combinatorial Problem