Answers are grounded in this paper and cite their sources.
This note considers the problem of sampling from the set of weighted independent sets of a graph with maximum degree Δ. For a positive fugacity λ, the weight of an independent set σ is λ|σ|. Luby and Vigoda proved that the Glauber dynamics, which only changes the configuration at a randomly chosen vertex in each step, has mixing time O(nlogn) when λ < 2 Δ-2 for triangle-free graphs. We extend their approach to general graphs.
No takes yet. Share an insight, caveat, or question.
Eric Vigoda (2001) studied this question.
Synapse has enriched 10 related papers. Consider them for comparative context: