Rémi Varloot
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.
The full paper is available on arXiv.
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Digital Library
- M. Huber. Perfect sampling using bounding chains. Ann. Appl. Probab., 14(2):734--753, 2004.Google ScholarCross Ref
- F. Pin, A. Bušić, and B. Gaujal. Acceleration of perfect sampling by skipping events. In Proceedings of the 5th International Conference on Performance Evaluation Methodologies and Tools (Valuetools), 2011. Google ScholarDigital Library
- J. G. Propp and D. B. Wilson. Exact sampling with coupled Markov chains and applications to statistical mechanics. Random Structures & Algorithms, 9(1--2):223--252, 1996. Google ScholarDigital Library
Index Terms
- Speeding up Glauber Dynamics for Random Generation of Independent Sets
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