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On Feedback Vertex Set New Measure and New Structures

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Algorithm Theory - SWAT 2010 (SWAT 2010)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 6139))

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Abstract

We study the parameterized complexity of the feedback vertex set problem (fvs) on undirected graphs. We approach the problem by considering a variation of it, the disjoint feedback vertex set problem (disjoint-fvs), which finds a disjoint feedback vertex set of size k when a feedback vertex set of a graph is given. We show that disjoint-fvs admits a small kernel, and can be solved in polynomial time when the graph has a special structure that is closely related to the maximum genus of the graph. We then propose a simple branch-and-search process on disjoint-fvs, and introduce a new branch-and-search measure. The branch-and-search process effectively reduces a given graph to a graph with the special structure, and the new measure more precisely evaluates the efficiency of the branch-and-search process. These algorithmic, combinatorial, and topological structural studies enable us to develop an O(3.83k kn 2) time parameterized algorithm for the general fvs problem, improving the previous best algorithm of time O(5k k n 2) for the problem.

Supported in part by the US NSF under the Grants CCF-0830455 and CCF-0917288.

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Author information

Authors and Affiliations

  1. Department of Computer Science and Engineering, Texas A&M University,  

    Yixin Cao & Jianer Chen

  2. Department of Computer Science, University of Texas - Pan American,  

    Yang Liu

Authors
  1. Yixin Cao
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  2. Jianer Chen
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  3. Yang Liu
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Editor information

Editors and Affiliations

  1. School of Computer Science, Tel Aviv University, 69978, Tel Aviv, Israel

    Haim Kaplan

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Cao, Y., Chen, J., Liu, Y. (2010). On Feedback Vertex Set New Measure and New Structures. In: Kaplan, H. (eds) Algorithm Theory - SWAT 2010. SWAT 2010. Lecture Notes in Computer Science, vol 6139. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-13731-0_10

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  • DOI: https://doi.org/10.1007/978-3-642-13731-0_10

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-13730-3

  • Online ISBN: 978-3-642-13731-0

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