A randomized approximation algorithm for metric triangle packing

Given an edge-weighted complete graph G on 3 n 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, i...

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Bibliographic Details
Published in:Journal of combinatorial optimization Vol. 41; no. 1; pp. 12 - 27
Main Authors: Chen, Yong, Chen, Zhi-Zhong, Lin, Guohui, Wang, Lusheng, Zhang, An
Format: Journal Article
Language:English
Published: New York Springer US 01.01.2021
Springer Nature B.V
Subjects:
Algorithms
Apexes
Approximation
Combinatorics
Convex and Discrete Geometry
Graph theory
Mathematical analysis
Mathematical Modeling and Industrial Mathematics
Mathematics
Mathematics and Statistics
Operations Research/Decision Theory
Optimization
Polynomials
Ratios
Theory of Computation
Weight
Metric
Maximum cycle cover
Approximation algorithm
Randomized algorithm
Triangle packing
ISSN:1382-6905, 1573-2886
Online Access:Get full text
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Summary:Given an edge-weighted complete graph G on 3 n 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 - ϵ for any constant ϵ > 0 .
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ISSN:1382-6905
1573-2886
DOI:10.1007/s10878-020-00660-7