On geometric matching

Authors:
O. Marcotte;S. Suri
Affiliations:
Département de mathématiques et d'informatique, Université du Québec à Montreal, C.P. 8888, Succ. "A", Montréal, Canada H3C 3P8;tBellcore, 445 South Street, Morristown, N.J.
Venue:
SCG '89 Proceedings of the fifth annual symposium on Computational geometry
Year:
1989

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Abstract

An &Ogr;(n3/2√&agr;(n)) time algorithm is presented for finding a minimum-weight matching of a set of 2n points lying on the boundary of a convex polygon, where &agr;(n) is the functional inverse of the Ackerman's function. Generalizing this result, we obtain an &Ogr;(n3/2 logn√&agr;(n)) time algorithm for the minimum-weight matching of points lying on the boundary of a simple nonconvex polygon, where we require that the line segments joining the matched pairs be contained within the polygon. We also consider the maximum-weight matching problem, and obtain algorithms of complexities &Ogr;(n) and &Ogr;(n log n) for the convex and the nonconvex case, respectively. By contrast, finding a weighted matching of an arbitrary set of points takes &Ogr;(n5/2 log4 n) time [Vaidya 1987].