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arXiv · 1911.10381

Smoothed complexity of local Max-Cut and binary Max-CSP

Xi Chen·Chenghao Guo·Emmanouil-Vasileios Vlatakis-Gkaragkounis·Mihalis Yannakakis·Xinzhi Zhang
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Abstract

We show that the smoothed complexity of the FLIP algorithm for local Max-Cut is at most $\smash{\phi n^{O(\sqrt{\log n})}}$, where $n$ is the number of nodes in the graph and $\phi$ is a parameter that measures the magnitude of perturbations applied on its edge weights. This improves the previously best upper bound of $\phi n^{O(\log n)}$ by Etscheid and R\"{o}glin. Our result is based on an analysis of long sequences of flips, which shows~that~it is very unlikely for every flip in a long sequence to incur a positive but small improvement in the cut weight. We also extend the same upper bound on the smoothed complexity of FLIP to all binary Maximum Constraint Satisfaction Problems.

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Xi Chen, Chenghao Guo, Emmanouil-Vasileios Vlatakis-Gkaragkounis, Mihalis Yannakakis, Xinzhi Zhang. 2019-11-23. Smoothed complexity of local Max-Cut and binary Max-CSP. https://arxiv.org/abs/1911.10381

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