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An Improved Approximation Algorithm for Metric Triangle Packing

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Theory and Applications of Models of Computation (TAMC 2024)

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Abstract

Given an edge-weighted metric complete graph with n vertices, the maximum weight metric triangle packing problem is to find a set of n/3 vertex-disjoint triangles with the total weight of all triangles in the packing maximized. Several simple methods can lead to a 2/3-approximation ratio. However, this barrier is not easy to break. Chen et al. proposed a randomized approximation algorithm with an expected ratio of \((0.66768-\varepsilon )\) for any constant \(\varepsilon >0\). In this paper, we improve the approximation ratio to \((0.66835-\varepsilon )\). Furthermore, we can derandomize our algorithm.

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Acknowledgments

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

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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. Chinese Academy of Sciences, Beijing, China

    Xujin Chen

  2. The Hong Kong Polytechnic University, Hong Kong, China

    Bo Li

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Zhao, J., Xiao, M. (2024). An Improved Approximation Algorithm for Metric Triangle Packing. In: Chen, X., Li, B. (eds) Theory and Applications of Models of Computation. TAMC 2024. Lecture Notes in Computer Science, vol 14637. Springer, Singapore. https://doi.org/10.1007/978-981-97-2340-9_5

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  • DOI: https://doi.org/10.1007/978-981-97-2340-9_5

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