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An O  ∗ (1.4786n)-Time Algorithm for the Maximum Induced Matching Problem

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Advances in Intelligent Systems and Applications - Volume 1

Part of the book series: Smart Innovation, Systems and Technologies ((SIST,volume 20))

Abstract

Given a graph G = (V, E) the Maximum r -Regular Induced Subgraph problem is to find a vertex set R ⊆ V of maximum cardinality such that G[R] is r-regular. An induced matching M ⊆ E in a graph G = (V, E) is a matching such that no two edges in M are joined by any third edge of the graph. The Maximum Induced Matching problem is to find an induced matching of maximum cardinality. By definition the maximum induced matching problem is the maximum 1-regular induced subgraph problem. Gupta et al. gave an o(2n) time algorithm for solving the Maximum r -Regular Induced Subgraph problem. This algorithm solves the Maximum Induced Matching problem in time O  ∗ (1.6957n) where n is the number of vertices in the input graph. In this paper, we show that the maximum induced matching problem can be reduced to the maximum independent set problem and we give a more efficient algorithm for the Maximum Induced Matching problem running in time O  ∗ (1.4786n).

This research is partially supported by the National Science Council of Taiwan under grants NSC 99–2221–E–241–015–MY3 and NSC 101–2221–E–241–019–MY3.

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Authors and Affiliations

  1. Department of Computer Science and Information Engineering, HungKuang University, 43302, Sha Lu, Taichung, Taiwan

    Maw-Shang Chang & Ling-Ju Hung

  2. Department of Computer Science and Information Engineering, National Chung Cheng University, 62102, Min-Hsiung, Chiayi, Taiwan

    Chau-An Miau

Authors
  1. Maw-Shang Chang
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  2. Ling-Ju Hung
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  3. Chau-An Miau
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Corresponding author

Correspondence to Maw-Shang Chang .

Editor information

Editors and Affiliations

  1. , Department of Computer Science and, National Dong Hwa University, #1, Sec. 2, Da Hsueh Rd., Hualien, Taiwan R.O.C.

    Ruay-Shiung Chang

  2. , Adjunct Professor, University of Canberra, Kirinari St. Mail Room, ACT, 2601, Australia

    Lakhmi C. Jain

  3. , Department of Computer Science and, National Dong Hwa University, #1, Sec. 2, Da Hsueh Rd., Hualien, Taiwan R.O.C.

    Sheng-Lung Peng

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Chang, MS., Hung, LJ., Miau, CA. (2013). An O  ∗ (1.4786n)-Time Algorithm for the Maximum Induced Matching Problem. In: Chang, RS., Jain, L., Peng, SL. (eds) Advances in Intelligent Systems and Applications - Volume 1. Smart Innovation, Systems and Technologies, vol 20. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-35452-6_7

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  • DOI: https://doi.org/10.1007/978-3-642-35452-6_7

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-35451-9

  • Online ISBN: 978-3-642-35452-6

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