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Improved Approximation Algorithms for Cycle and Path Packings

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WALCOM: Algorithms and Computation (WALCOM 2024)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 14549))

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Abstract

Given an edge-weighted (metric/general) complete graph with n vertices, the maximum weight (metric/general) k-cycle/path packing problem is to find a set of \(\frac{n}{k}\) vertex-disjoint k-cycles/paths such that the total weight is maximized. In this paper, we consider approximation algorithms. For metric k-cycle packing, we improve the previous approximation ratio from 3/5 to 7/10 for \(k=5\), and from \(7/8\cdot (1-1/k)^2\) for \(k>5\) to \((7/8-0.125/k)(1-1/k)\) for constant odd \(k>5\) and to \(7/8\cdot (1-1/k+\frac{1}{k(k-1)})\) for even \(k>5\). For metric k-path packing, we improve the approximation ratio from \(7/8\cdot (1-1/k)\) to \(\frac{27k^2-48k+16}{32k^2-36k-24}\) for even \(10\ge k\ge 6\). For the case of \(k=4\), we improve the approximation ratio from 3/4 to 5/6 for metric 4-cycle packing, from 2/3 to 3/4 for general 4-cycle packing, and from 3/4 to 14/17 for metric 4-path packing.

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Acknowledgments

The work is supported by the National Natural Science Foundation of China, under grants 62372095 and 61972070.

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Authors and Affiliations

  1. University of Electronic Science and Technology of China, Chengdu, China

    Jingyang Zhao & Mingyu Xiao

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  1. Jingyang Zhao
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  2. Mingyu Xiao
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Correspondence to Mingyu Xiao .

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Editors and Affiliations

  1. Japan Advanced Institute of Science and Technology, Nomi, Japan

    Ryuhei Uehara

  2. Iwate University, Morioka, Japan

    Katsuhisa Yamanaka

  3. National Taiwan University, Taipei, Taiwan

    Hsu-Chun Yen

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Zhao, J., Xiao, M. (2024). Improved Approximation Algorithms for Cycle and Path Packings. In: Uehara, R., Yamanaka, K., Yen, HC. (eds) WALCOM: Algorithms and Computation. WALCOM 2024. Lecture Notes in Computer Science, vol 14549. Springer, Singapore. https://doi.org/10.1007/978-981-97-0566-5_14

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  • DOI: https://doi.org/10.1007/978-981-97-0566-5_14

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  • Print ISBN: 978-981-97-0565-8

  • Online ISBN: 978-981-97-0566-5

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