加速Glauber动力学随机生成独立集
Speeding up Glauber Dynamics for Random Generation of Independent Sets
摘要：
最大独立集（MIS）问题是一个广泛研究的组合优化问题，它在无线通信、信息论和统计力学等领域有着广泛的应用。MIS问题是NP难的，因此文献中的许多结果都集中在快速生成高基数的极大独立集。一种可能性是结合吉布斯采样与耦合从过去的论点，以检测收敛到固定制度。这导致采样过程的时间复杂度取决于Glauber动力学马尔可夫链的混合时间。我们提出了一种自适应的方法，在Glauber动力学的随机事件生成，只考虑从过去的计划，加速吉布斯采样算法的收敛时间的耦合有效的事件。
英文摘要：
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.
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