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Open Access

Approximation Algorithms for Graph Partition into Bounded Independent Sets

Department of Mathematics, Hangzhou Dianzi University, Hangzhou 310018, China
Zhejiang University of Water Resources and Electric Power, Hangzhou 310018, China
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Abstract

The partition problem of a given graph into three independent sets of minimizing the maximum one is studied in this paper. This problem is NP-hard, even restricted to bipartite graphs. First, a simple 32-approximation algorithm for any 2-colorable graph is presented. An improved 75-approximation algorithm is then designed for a tree. The theoretical proof of the improved algorithm performance ratio is constructive, thus providing an explicit partition approach for each case according to the cardinality of two color classes.

Keywords

graph partitionindependent set2-colorable graphapproximation algorithm

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Tsinghua Science and Technology
Volume 28 Issue 6,
December 2023
Pages 1063-1071
DOI: 10.26599/TST.2022.9010062
Cite this article:
Xie J, Chen Y, Zhang A, et al. Approximation Algorithms for Graph Partition into Bounded Independent Sets. Tsinghua Science and Technology, 2023, 28(6): 1063-1071. https://doi.org/10.26599/TST.2022.9010062

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Received: 15 September 2022
Revised: 04 December 2022
Accepted: 05 December 2022
Published: 28 July 2023
© The author(s) 2023.

The articles published in this open access journal are distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/).
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