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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 graph k-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–min k-BGP (min–max k-BGP, respectively), and has received much study since about four decades ago. On general graphs, max–min k-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, 2022. "Approximation algorithms for the maximally balanced connected graph tripartition problem," Journal of Combinatorial Optimization, Springer, vol. 44(3), pages 1753-1773, October.
    • Handle: RePEc:spr:jcomop:v:44:y:2022:i:3: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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