Volume 1350 of the series Lecture Notes in Computer Science pp 384393
A branchandcut approach for minimum weight triangulation
 Yoshiaki KyodaAffiliated withDepartment of Information Science, University of Tokyo
 , Keiko ImaiAffiliated withDepartment of Information and System Engineering, Chuo University
 , Fumihiko TakeuchiAffiliated withDepartment of Information Science, University of Tokyo
 , Akira TajimaAffiliated withIBM Tokyo Research Laboratory
Abstract
This paper considers the problem of computing a minimum weight triangulation of n points in the plane, which has been intensively studied in recent years in computational geometry. This paper investigates a branchandcut approach for minimum weight triangulations. The problem can be formulated as finding a minimumweight maximal independent set of intersection graphs of edges. In combinatorial optimization, there are known many cuts for the independent set problem, and we further use a cut induced by geometric properties of triangulations. Combining this branchandcut approach with the βskeleton method, the moderatesize problem could be solved efficiently in our computational experiments. Polyhedral characterizations of the proposed cut and applications of another old skeletal approach in mathematical programming as the independent set problem are also touched upon.
 Title
 A branchandcut approach for minimum weight triangulation
 Book Title
 Algorithms and Computation
 Book Subtitle
 8th International Symposium, ISAAC '97 Singapore, December 17–19, 1997 Proceedings
 Pages
 pp 384393
 Copyright
 1997
 DOI
 10.1007/3540638903_41
 Print ISBN
 9783540638902
 Online ISBN
 9783540696629
 Series Title
 Lecture Notes in Computer Science
 Series Volume
 1350
 Series ISSN
 03029743
 Publisher
 Springer Berlin Heidelberg
 Copyright Holder
 SpringerVerlag
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 Editors
 Authors

 Yoshiaki Kyoda ^{(1)}
 Keiko Imai ^{(2)}
 Fumihiko Takeuchi ^{(1)}
 Akira Tajima ^{(3)}
 Author Affiliations

 1. Department of Information Science, University of Tokyo, Japan
 2. Department of Information and System Engineering, Chuo University, Japan
 3. IBM Tokyo Research Laboratory, Japan
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