Abstract
A linear programming relaxation of the minimal matching problem is studied for graphs with edge weights determined by the distances between points in a Euclidean space. The relaxed problem has a simple geometric interpretation that suggests the name minimal semi-matching. The main result is the determination of the asymptotic behavior of the length of the minimal semi-matching. It is analogous to the theorem of Beardwood, Halton and Hammersley (1959) on the asymptotic behavior of the traveling salesman problem. Associated results on the length of non-random Euclidean semi-matchings and large deviation inequalities for random semi-matchings are also given.
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Research supported in part by NSF Grant #DMS-8812868, ARO contract DAAL03-89-G-0092.P001, AFOSR-89-08301.A and NSA-MDA-904-89-2034.
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Steele, J.M. Euclidean semi-matchings of random samples. Mathematical Programming 53, 127–146 (1992). https://doi.org/10.1007/BF01585699
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DOI: https://doi.org/10.1007/BF01585699