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

Julie Delon (1) , Julien Salomon (2) , Andrei Sobolevski (3, 4)

1 LTCI - Laboratoire Traitement et Communication de l'Information
2 CEREMADE - CEntre de REcherches en MAthématiques de la DEcision
3 ISCP - Interdisciplinary Scientific Center Poncelet
4 IITP - Kharkevich Institute for Information Transmission Problems

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.

Mots clés: matching; graph; metric space

Domaines: Optimisation et contrôle [math.OC]

Julie Delon, Julien Salomon, Andrei Sobolevski. Minimum-weight perfect matching for non-intrinsic distances on the line. 2011. ⟨hal-00564173v2⟩