Minimum-weight perfect matching for non-intrinsic distances on the line
arXiv:1102.1558 · doi:10.1007/s10958-012-0714-6
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.
13 pages, figures in TiKZ, uses xcolor package; introduction and the concluding section have been expanded