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A Measure and Conquer Approach for the Parameterized Bounded Degree-One Vertex Deletion

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Computing and Combinatorics (COCOON 2015)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 9198))

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Abstract

Measure & Conquer is an approach helpful for designing branching algorithms. A key point in the approach is how to design the measure. Given a graph \(G=(V,E)\) and an integer k, the Bounded Degree-one Deletion problem asks for if there exists a subset D of at most k vertices such that the degree of any vertex in \(G[V\setminus D]\) is upper bounded by one. Combining the parameter with a potential as the measure in Measure & Conquer, where the potential is a lower bound of the decrement of the parameter, we design a branching algorithm running in polynomial space and \(O(1.882^k+|V||E|)\) time, which improves the current best parameterized complexity \(O^*(2^k)\) of the problem.

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Author information

Authors and Affiliations

  1. National Chung Cheng University, Chiayi, 621, Taiwan, R.O.C

    Bang Ye Wu

Authors
  1. Bang Ye Wu
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Correspondence to Bang Ye Wu .

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Editors and Affiliations

  1. Beijing University of Technology, Beijing, China

    Dachuan Xu

  2. University of New Brunswick, Fredericton, Canada

    Donglei Du

  3. University of Texas at Dallas, Richardson, USA

    Dingzhu Du

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Wu, B.Y. (2015). A Measure and Conquer Approach for the Parameterized Bounded Degree-One Vertex Deletion. In: Xu, D., Du, D., Du, D. (eds) Computing and Combinatorics. COCOON 2015. Lecture Notes in Computer Science(), vol 9198. Springer, Cham. https://doi.org/10.1007/978-3-319-21398-9_37

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  • DOI: https://doi.org/10.1007/978-3-319-21398-9_37

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-21397-2

  • Online ISBN: 978-3-319-21398-9

  • eBook Packages: Computer ScienceComputer Science (R0)

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