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

Julie Delon; Julien Salomon; Andrei Sobolevski

hal-00564173, version 2

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

Julie Delon () ¹, Julien Salomon () ², Andrei Sobolevski ( Author to contact preferably ) ^3, 4

(2011-03-26)

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.

1: Laboratoire Traitement et Communication de l'Information [Paris] (LTCI)
Télécom ParisTech – CNRS : UMR5141
2: CEntre de REcherches en MAthématiques de la DEcision (CEREMADE)
CNRS : UMR7534 – Université Paris IX - Paris Dauphine
3: Laboratoire J.-V. Poncelet (LIFR-MI2P)
CNRS : UMI2615 – Independent University of Moscow
4: A.A.Kharkevich Institute for Information Transmission Problems
Russian Academy of Science

hal-00564173, version 2
http://hal.archives-ouvertes.fr/hal-00564173
oai:hal.archives-ouvertes.fr:hal-00564173
From: Andrei Sobolevskii <>
Submitted on: Saturday, 26 March 2011 16:06:56
Updated on: Saturday, 26 March 2011 21:20:17

See detailed view

Associated documents

PDF :

PS :

arXiv: 1102.1558

Export

Bibtex EndNote TEI RefWorks

<?xml version="1.0" encoding="UTF-8"?>
<listBibl xmlns="http://www.tei-c.org/ns/1.0" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:mml="http://www.w3.org/1998/Math/MathML">
<listBibl type="article"><head>Documents without publication reference (Preprint)</head>
<biblStruct type="article" xml:id="hal-00564173"><analytic>
<author><persName><forename>Julie</forename><surname>Delon</surname></persName>
<affiliation>
<orgName type="laboratory">LTCI</orgName>
<orgName type="team">Laboratoire Traitement et Communication de l'Information [Paris]</orgName>
<country>FR</country>
<orgName type="institution">Télécom ParisTech</orgName>
<orgName type="institution">CNRS : UMR5141</orgName>
</affiliation>
</author>
<author><persName><forename>Julien</forename><surname>Salomon</surname></persName>
<affiliation>
<orgName type="laboratory">CEREMADE</orgName>
<orgName type="team">CEntre de REcherches en MAthématiques de la DEcision</orgName>
<country>FR</country>
<orgName type="institution">CNRS : UMR7534</orgName>
<orgName type="institution">Université Paris IX - Paris Dauphine</orgName>
</affiliation>
</author>
<author><persName><forename>Andrei</forename><surname>Sobolevski</surname></persName>
<affiliation>
<orgName type="laboratory">LIFR-MI2P</orgName>
<orgName type="team">Laboratoire J.-V. Poncelet</orgName>
<country>RU</country>
<orgName type="institution">CNRS : UMI2615</orgName>
<orgName type="institution">Independent University of Moscow</orgName>
</affiliation>
<affiliation>
<orgName type="team">A.A.Kharkevich Institute for Information Transmission Problems</orgName>
<country>RU</country>
<orgName type="institution">Russian Academy of Science</orgName>
</affiliation>
</author>
<title type="main" level="a">Minimum-weight perfect matching for non-intrinsic distances on the line</title></analytic><monogr><imprint/></monogr><idno type="HALid">http://hal.archives-ouvertes.fr/hal-00564173</idno><idno type="HALFile">http://hal.archives-ouvertes.fr/hal-00564173/PDF/JSSrecursion2.pdf</idno></biblStruct>
</listBibl>
</listBibl>