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

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

2011-02-08

arxiv.org/abs/1102.1558v2

Mathematics

Optimization and Control

13 pages, figures in TiKZ, uses xcolor package; introduction and the concluding section have been expanded

Scientific paper

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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