Fast Approximation Algorithms for Euclidean Minimum Weight Perfect Matching

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Abstract

We study the problem of finding a Euclidean minimum weight perfect matching for n points in the plane. It is known that a deterministic approximation algorithm for this problems must have at least (n n) runtime. We propose such an algorithm for the Euclidean minimum weight perfect matching problem with runtime O (n n) and show that it has approximation ratio O (n^0. 2995). This improves the so far best known approximation ratio of n/2. We also develop an O (n n) algorithm for the Euclidean minimum weight perfect matching problem in higher dimensions and show it has approximation ratio O (n^0. 599) in all fixed dimensions.

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Hougardy et al. (Wed,) studied this question.

synapsesocial.com/papers/68e60ce9b6db6435875a04e4 https://doi.org/https://doi.org/10.48550/arxiv.2407.07749

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