This note considers the problem of sampling from the set of weighted independent sets of a graph with maximum degree ∆. 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(n log n) when λ < 2 ∆−2 for triangle-free graphs. We extend their approach to general graphs.
For general graphs, the state-of-the-art was given by REF , which showed the Glauber dynamics mixes in O(n log n) steps when λ < 2 ∆−2 .
A Note on the Glauber Dynamics for Sampling Independent Sets
Electr. J. Comb.
Mathematics Computer Science