A Randomized Approximation Algorithm for Metric Triangle Packing

Yong Chen,Zhi-Zhong Chen,Lusheng Wang,An Zhang,Guohui Lin

doi:10.1007/978-3-030-36412-0_10

A Randomized Approximation Algorithm for Metric Triangle Packing

Yong Chen, Zhi-Zhong Chen + Show 3 more

https://doi.org/10.1007/978-3-030-36412-0_10

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Publication Date: Jan 1, 2019

Affiliation: Hangzhou Dianzi University, Tokyo Denki University, City University of Hong Kong, University of Alberta

#Nontrivial Approximation Algorithm #Total Weight Of Edges + Show 8 more

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Abstract

Given an edge-weighted complete graph G on 3n vertices, the maximum-weight triangle packing problem (MWTP for short) 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 MWTP 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 (denoted by MMWTP), 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 MMWTP. Our algorithm is randomized and achieves an expected approximation ratio of \(0.66745 - \epsilon \) for any constant \(\epsilon > 0\).

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