A randomized approximation algorithm for metric triangle packing

Yong Chen (), Zhi-Zhong Chen (), Guohui Lin (), Lusheng Wang () and An Zhang
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Yong Chen: Hangzhou Dianzi University
Zhi-Zhong Chen: Tokyo Denki University
Guohui Lin: University of Alberta
Lusheng Wang: City University of Hong Kong
An Zhang: Hangzhou Dianzi University

Journal of Combinatorial Optimization, 2021, vol. 41, issue 1, No 2, 12-27

Abstract: Abstract Given an edge-weighted complete graph G on 3n vertices, the maximum-weight triangle packing problem asks for a collection of n vertex-disjoint triangles in G such that the total weight of edges in these n triangles is maximized. Although the problem has been extensively studied in the literature, it is surprising that prior to this work, no nontrivial approximation algorithm had been designed and analyzed for its metric case, where the edge weights in the input graph satisfy the triangle inequality. In this paper, we design the first nontrivial polynomial-time approximation algorithm for the maximum-weight metric triangle packing problem. Our algorithm is randomized and achieves an expected approximation ratio of $$0.66768 - \epsilon $$ 0.66768 - ϵ for any constant $$\epsilon > 0$$ ϵ > 0 .

Keywords: Triangle packing; Metric; Approximation algorithm; Randomized algorithm; Maximum cycle cover (search for similar items in EconPapers)
Date: 2021
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DOI: 10.1007/s10878-020-00660-7

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