Approximation Algorithms for Maximally Balanced Connected Graph Partition View Full Text


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Article Info

DATE

2021-09-12

AUTHORS

Yong Chen, Zhi-Zhong Chen, Guohui Lin, Yao Xu, An Zhang

ABSTRACT

Given a connected graph G=(V,E)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$G = (V, E)$$\end{document}, we seek to partition the vertex set V into k non-empty parts such that the subgraph induced by each part is connected, and the partition is maximally balanced in the way that the maximum cardinality of these k parts is minimized. We refer this problem to as min-max balanced connected graph partition into k parts and denote it as k-BGP. The vertex-weighted version of this problem on trees has been studied since about four decades ago, which admits a linear time exact algorithm. The vertex-weighted 2-BGP and 3-BGP admit a 5/4-approximation and a 3/2-approximation, respectively. When k≥4\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$k \ge 4$$\end{document}, no approximability result exists for k-BGP, i.e., the vertex unweighted variant, except a trivial k-approximation. In this paper, we present another 3/2-approximation for the 3-BGP and then extend it to become a k/2-approximation for k-BGP, for any fixed k≥3\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$k \ge 3$$\end{document}. Furthermore, for 4-BGP, we propose an improved 24/13-approximation. To these purposes, we have designed several local improvement operations, which could find more applications in related graph partition problems. More... »

PAGES

3715-3740

References to SciGraph publications

  • 2020-02-17. Approximation algorithms for the maximally balanced connected graph tripartition problem in JOURNAL OF COMBINATORIAL OPTIMIZATION
  • 2018-03-21. Efficient Algorithms for a Graph Partitioning Problem in FRONTIERS IN ALGORITHMICS
  • 2013-01-03. Max-min weight balanced connected partition in JOURNAL OF GLOBAL OPTIMIZATION
  • 2011. A 7/6-Approximation Algorithm for the Max-Min Connected Bipartition Problem on Grid Graphs in COMPUTATIONAL GEOMETRY, GRAPHS AND APPLICATIONS
  • Identifiers

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    http://scigraph.springernature.com/pub.10.1007/s00453-021-00870-3

    DOI

    http://dx.doi.org/10.1007/s00453-021-00870-3

    DIMENSIONS

    https://app.dimensions.ai/details/publication/pub.1141065848


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