Speeding up Glauber Dynamics for Random Generation of Independent Sets

TL;DR

This paper introduces an adaptive method to accelerate Glauber dynamics for generating large independent sets efficiently, reducing convergence time by focusing only on effective events during sampling.

Contribution

It presents a novel adaptive approach that improves the efficiency of Gibbs sampling for the MIS problem by optimizing the coupling from the past process.

Findings

Accelerates convergence of Glauber dynamics

Reduces computational complexity in sampling

Enhances efficiency in generating high-cardinality independent sets

Abstract

The maximum independent set (MIS) problem is a well-studied combinatorial optimization problem that naturally arises in many applications, such as wireless communication, information theory and statistical mechanics. MIS problem is NP-hard, thus many results in the literature focus on fast generation of maximal independent sets of high cardinality. One possibility is to combine Gibbs sampling with coupling from the past arguments to detect convergence to the stationary regime. This results in a sampling procedure with time complexity that depends on the mixing time of the Glauber dynamics Markov chain. We propose an adaptive method for random event generation in the Glauber dynamics that considers only the events that are effective in the coupling from the past scheme, accelerating the convergence time of the Gibbs sampling algorithm.