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Approximation algorithms for the maximally balanced connected graph tripartition problem

Author

Listed:
  • Guangting Chen

    (Taizhou University)

  • Yong Chen

    (Hangzhou Dianzi University)

  • Zhi-Zhong Chen

    (Tokyo Denki University)

  • Guohui Lin

    (University of Alberta)

  • Tian Liu

    (Peking University)

  • An Zhang

    (Hangzhou Dianzi University)

Abstract

Given a vertex-weighted connected graph $$G = (V, E, w(\cdot ))$$G=(V,E,w(·)), the maximally balanced connected graphk-partition (k-BGP) seeks to partition the vertex set V into k non-empty parts such that the subgraph induced by each part is connected and the weights of these k parts are as balanced as possible. When the concrete objective is to maximize the minimum (to minimize the maximum, respectively) weight of the k parts, the problem is denoted as max–mink-BGP (min–maxk-BGP, respectively), and has received much study since about four decades ago. On general graphs, max–mink-BGP is strongly NP-hard for every fixed $$k \ge 2$$k≥2, and remains NP-hard even for the vertex uniformly weighted case; when k is part of the input, the problem is denoted as max–min BGP, and cannot be approximated within 6/5 unless P $$=$$= NP. In this paper, we study the tripartition problems from approximation algorithms perspective and present a 3/2-approximation for min–max 3-BGP and a 5/3-approximation for max–min 3-BGP, respectively. These are the first non-trivial approximation algorithms for 3-BGP, to our best knowledge.

Suggested Citation

  • Guangting Chen & Yong Chen & Zhi-Zhong Chen & Guohui Lin & Tian Liu & An Zhang, 0. "Approximation algorithms for the maximally balanced connected graph tripartition problem," Journal of Combinatorial Optimization, Springer, vol. 0, pages 1-21.
    • Handle: RePEc:spr:jcomop:v::y::i::d:10.1007_s10878-020-00544-w
    DOI: 10.1007/s10878-020-00544-w
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    References listed on IDEAS

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    1. Lele Wang & Zhao Zhang & Di Wu & Weili Wu & Lidan Fan, 2013. "Max-min weight balanced connected partition," Journal of Global Optimization, Springer, vol. 57(4), pages 1263-1275, December.
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    Cited by:

    1. Miyazawa, Flávio K. & Moura, Phablo F.S. & Ota, Matheus J. & Wakabayashi, Yoshiko, 2021. "Partitioning a graph into balanced connected classes: Formulations, separation and experiments," European Journal of Operational Research, Elsevier, vol. 293(3), pages 826-836.

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    1. Guangting Chen & Yong Chen & Zhi-Zhong Chen & Guohui Lin & Tian Liu & An Zhang, 2022. "Approximation algorithms for the maximally balanced connected graph tripartition problem," Journal of Combinatorial Optimization, Springer, vol. 44(3), pages 1753-1773, October.

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