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An Exact Algorithm for Maximum Independent Set in Degree-5 Graphs

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Frontiers in Algorithmics and Algorithmic Aspects in Information and Management

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 7924))

Abstract

The maximum independent set problem is a basic NP-hard problem and has been extensively studied in exact algorithms. The maximum independent set problems in low-degree graphs are also important and may be bottlenecks of the problem in general graphs. In this paper, we present an O *(1.1737n)-time exact algorithm for the maximum independent set problem in an n-vertex graph with degree bounded by 5, improving the previous running time bound of O *(1.1895n). In our algorithm, we introduce an effective divide-and-conquer procedure to deal with vertex cuts of size at most two in graphs, and design branching rules on some special structures of triconnected graphs of maximum degree 5. These result in an improved algorithm without introducing a large number of branching rules.

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Author information

Authors and Affiliations

  1. School of Computer Science and Engineering, University of Electronic Science and Technology of China, China

    Mingyu Xiao

  2. Department of Applied Mathematics and Physics, Graduate School of Informatics, Kyoto University, Japan

    Hiroshi Nagamochi

Authors
  1. Mingyu Xiao
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  2. Hiroshi Nagamochi
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Editor information

Editors and Affiliations

  1. School of Engineering and Information Technology, Charles Darwin University, 0909, Darwin, NT, Australia

    Michael Fellows

  2. School of High-Technology for Human Welfare, Tokai University, 317 Nishimo, 410-0395, Numazu, Japan

    Xuehou Tan

  3. Department of Computer Science, Montana State University, 59717, Bozeman, MT, USA

    Binhai Zhu

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Xiao, M., Nagamochi, H. (2013). An Exact Algorithm for Maximum Independent Set in Degree-5 Graphs. In: Fellows, M., Tan, X., Zhu, B. (eds) Frontiers in Algorithmics and Algorithmic Aspects in Information and Management. Lecture Notes in Computer Science, vol 7924. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-38756-2_10

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  • DOI: https://doi.org/10.1007/978-3-642-38756-2_10

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-38755-5

  • Online ISBN: 978-3-642-38756-2

  • eBook Packages: Computer ScienceComputer Science (R0)

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