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Almost Induced Matching: Linear Kernels and Parameterized Algorithms

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Graph-Theoretic Concepts in Computer Science (WG 2016)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 9941))

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Abstract

The Almost Induced Matching problem asks whether we can delete at most k vertices from a graph such that the remaining graph is an induced matching, i.e., a graph with each vertex of degree 1. This paper studies parameterized algorithms for this problem by taking the size of deletion set k as the parameter. By using the techniques of finding maximal 3-path packings and an extended crown decomposition, we obtain the first linear vertex kernel for this problem, improving the previous quadratic kernel. We also present an \(O^*(1.7485^k)\)-time and polynomial-space algorithm, which is the best known parameterized algorithm for this problem.

This work is supported by the National Natural Science Foundation of China, under grant 61370071, and the Fundamental Research Funds for the Central Universities, under grant ZYGX2015J057.

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Authors and Affiliations

  1. School of Computer Science and Engineering, UESTC, Chengdu, 611731, China

    Mingyu Xiao & Shaowei Kou

  2. Center for Information in Medicine, UESTC, Chengdu, 611731, China

    Mingyu Xiao

Authors
  1. Mingyu Xiao
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  2. Shaowei Kou
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Corresponding author

Correspondence to Mingyu Xiao .

Editor information

Editors and Affiliations

  1. University of Bergen, Bergen, Norway

    Pinar Heggernes

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Xiao, M., Kou, S. (2016). Almost Induced Matching: Linear Kernels and Parameterized Algorithms. In: Heggernes, P. (eds) Graph-Theoretic Concepts in Computer Science. WG 2016. Lecture Notes in Computer Science(), vol 9941. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-53536-3_19

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  • DOI: https://doi.org/10.1007/978-3-662-53536-3_19

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-662-53535-6

  • Online ISBN: 978-3-662-53536-3

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