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arXiv · 2108.12840

Exact algorithms for maximum weighted independent set on sparse graphs

Sen Huang·Mingyu Xiao·Xiaoyu Chen
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Abstract

The maximum independent set problem is one of the most important problems in graph algorithms and has been extensively studied in the line of research on the worst-case analysis of exact algorithms for NP-hard problems. In the weighted version, each vertex in the graph is associated with a weight and we are going to find an independent set of maximum total vertex weight. In this paper, we design several reduction rules and a fast exact algorithm for the maximum weighted independent set problem, and use the measure-and-conquer technique to analyze the running time bound of the algorithm. Our algorithm works on general weighted graphs and it has a good running time bound on sparse graphs. If the graph has an average degree at most 3, our algorithm runs in $O^*(1.1443^n)$ time and polynomial space, improving previous running time bounds for the problem in cubic graphs using polynomial space.

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Sen Huang, Mingyu Xiao, Xiaoyu Chen. 2021-08-29. Exact algorithms for maximum weighted independent set on sparse graphs. https://arxiv.org/abs/2108.12840

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