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Approximate minimum weight matching on points ink-dimensional space

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Abstract

We study the problem of finding a minimum weight complete matching in the complete graph on a set V ofn points ink-dimensional space. The points are the vertices of the graph and the weight of an edge between any two points is the distance between the points under someL q,-metric. We give anO((2c q )1.5kɛ−1.5k(α(n, n))0.5 n 1.5(logn)2.5) algorithm for finding an almost minimum weight complete matching in such a graph, wherec q =6k 1/q for theL q -metric, α is the inverse Ackermann function, and ɛ ≤ 1. The weight of the complete matching obtained by our algorithm is guaranteed to be at most (1 + ɛ) times the weight of a minimum weight complete matching.

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Authors and Affiliations

  1. 2D-153, AT&T Bell Laboratories, 600 Mountain Avenue, 07974, Murray Hill, NJ, USA

    Pravin M. Vaidya

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  1. Pravin M. Vaidya
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Communicated by C. K. Wong.

This research was supported by a fellowship from the Shell Foundation.

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Vaidya, P.M. Approximate minimum weight matching on points ink-dimensional space. Algorithmica 4, 569–583 (1989). https://doi.org/10.1007/BF01553909

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  • DOI: https://doi.org/10.1007/BF01553909

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