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.Comment: 13 pages, figures in TiKZ, uses xcolor package; introduction and the
concluding section have been expande
