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arXiv · 1102.1558

Minimum-weight perfect matching for non-intrinsic distances on the line

Julie Delon·Julien Salomon·Andrei Sobolevski
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Abstract

Consider a real line equipped with a (not necessarily intrinsic) distance. We deal with the minimum-weight perfect matching problem for a complete graph whose points are located on the line and whose edges have weights equal to distances along the line. This problem is closely related to one-dimensional Monge-Kantorovich trasnport optimization. The main result of the present note is a "bottom-up" recursion relation for weights of partial minimum-weight matchings.

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Julie Delon, Julien Salomon, Andrei Sobolevski. 2011-03-26. Minimum-weight perfect matching for non-intrinsic distances on the line. https://doi.org/10.1007/s10958-012-0714-6

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