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A New Kernel for Parameterized Max-Bisection Above Tight Lower Bound

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Computing and Combinatorics (COCOON 2017)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 10392))

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Abstract

In this paper, we study kernelization of Parameterized Max-Bisection above Tight Lower Bound problem, which is to find a bisection \((V_1, V_2)\) of G with at least \(\lceil |E|/2\rceil +k\) crossing edges for a given graph \(G=(V, E)\). The current best vertex kernel result for the problem is of size 16k. Based on analysis of the relation between maximum matching and vertices in Gallai-Edmonds decomposition of G, we divide graph G into a set of blocks, and each block in G is closely related to the number of crossing edges of bisection of G. By analyzing the number of crossing edges in all blocks, an improved vertex kernel of size 8k is presented.

This work is supported by the National Natural Science Foundation of China under Grants (61420106009, 61232001, 61472449, 61672536, 61572414).

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Authors and Affiliations

  1. School of Information Science and Engineering, Central South University, Changsha, 410083, People’s Republic of China

    Qilong Feng, Senmin Zhu & Jianxin Wang

Authors
  1. Qilong Feng
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  2. Senmin Zhu
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  3. Jianxin Wang
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Corresponding author

Correspondence to Jianxin Wang .

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Editors and Affiliations

  1. Department of Computing, Hong Kong Polytechnic University, Hong Kong, China

    Yixin Cao

  2. Texas A&M University, College Station, Texas, USA

    Jianer Chen

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Feng, Q., Zhu, S., Wang, J. (2017). A New Kernel for Parameterized Max-Bisection Above Tight Lower Bound. In: Cao, Y., Chen, J. (eds) Computing and Combinatorics. COCOON 2017. Lecture Notes in Computer Science(), vol 10392. Springer, Cham. https://doi.org/10.1007/978-3-319-62389-4_16

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  • DOI: https://doi.org/10.1007/978-3-319-62389-4_16

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-62388-7

  • Online ISBN: 978-3-319-62389-4

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