Euclidean semi-matchings of random samples

A linear programming relaxation of the minimal matching problem is studied for graphs with edge weights determined by the distances between points in a Euclidean space. The relaxed problem has a simple geometric interpretation that suggests the name minimal semi-matching. The main result is the dete...

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Bibliographic Details
Published inMathematical programming Vol. 53; no. 1-3; pp. 127 - 146
Main Author Steele, J. Michael
Format Journal Article
LanguageEnglish
Published Heidelberg Springer 01.01.1992
Subjects
Applied sciences
Exact sciences and technology
Flows in networks. Combinatorial problems
Operational research and scientific management
Operational research. Management science
Asymptotic behavior
Travelling salesman problem
Relaxation method
Linear programming
Graph theory
Convergence
Graph matching
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Summary:A linear programming relaxation of the minimal matching problem is studied for graphs with edge weights determined by the distances between points in a Euclidean space. The relaxed problem has a simple geometric interpretation that suggests the name minimal semi-matching. The main result is the determination of the asymptotic behavior of the length of the minimal semi-matching. It is analogous to the theorem of Beardwood, Halton and Hammersley (1959) on the asymptotic behavior of the traveling salesman problem. Associated results on the length of non-random Euclidean semi-matchings and large deviation inequalities for random semi-matchings are also given.
Bibliography:ObjectType-Article-2
SourceType-Scholarly Journals-1
ObjectType-Feature-1
content type line 23
ISSN:0025-5610
1436-4646
DOI:10.1007/BF01585699