Approximation Algorithms for Maximally Balanced Connected Graph Partition

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

Research output: Contribution to journalArticlepeer-review

6 Scopus citations

Abstract

Given a connected graph G= (V, E) , 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 , 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. 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.

Original languageEnglish
Pages (from-to)3715-3740
Number of pages26
JournalAlgorithmica
Volume83
Issue number12
DOIs
StatePublished - Dec 2021

Keywords

  • Approximation algorithm
  • Connected component
  • Graph partition
  • Induced subgraph
  • Local improvement

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