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International Computing and Combinatorics Conference

COCOON 2021: Computing and Combinatorics pp 617–628Cite as

Exact Algorithms for Maximum Weighted Independent Set on Sparse Graphs (Extended Abstract)

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Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 13025))

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.

The work is supported by the National Natural Science Foundation of China, under grant 61972070.

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Author information

Authors and Affiliations

  1. University of Electronic Science and Technology of China, Chengdu, China

    Sen Huang & Mingyu Xiao

  2. Nanjing University, Nanjing, China

    Xiaoyu Chen

Authors
  1. Sen Huang
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  2. Mingyu Xiao
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  3. Xiaoyu Chen
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Editor information

Editors and Affiliations

  1. National Cheng Kung University, Tainan, Taiwan

    Chi-Yeh Chen

  2. National Tsing Hua University, Hsinchu, Taiwan

    Wing-Kai Hon

  3. National Taipei University of Business, Taoyuan, Taiwan

    Ling-Ju Hung

  4. National Taitung University, Taitung, Taiwan

    Chia-Wei Lee

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Huang, S., Xiao, M., Chen, X. (2021). Exact Algorithms for Maximum Weighted Independent Set on Sparse Graphs (Extended Abstract). In: Chen, CY., Hon, WK., Hung, LJ., Lee, CW. (eds) Computing and Combinatorics. COCOON 2021. Lecture Notes in Computer Science(), vol 13025. Springer, Cham. https://doi.org/10.1007/978-3-030-89543-3_51

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  • DOI: https://doi.org/10.1007/978-3-030-89543-3_51

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-89542-6

  • Online ISBN: 978-3-030-89543-3

  • eBook Packages: Computer ScienceComputer Science (R0)

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