Polynomial-time instances of the minimum weight triangulation problem
نویسندگان
چکیده
منابع مشابه
Solving Large-Scale Minimum-Weight Triangulation Instances to Provable Optimality
We consider practical methods for the problem of finding a minimum-weight triangulation (MWT) of a planar point set, a classic problem of computational geometry with many applications. While Mulzer and Rote proved in 2006 that computing an MWT is NP-hard, Beirouti and Snoeyink showed in 1998 that computing provably optimal solutions for MWT instances of up to 80,000 uniformly distributed points...
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The original version of this paper was published as Technical Report LU-CS-TR:2005-238 on February 13, 2006, ISSN 1650-1276 Report 158, Lund University, Sweden 2006. This is an extended version published on February 20, 2006. We discuss and compare four fixed parameter algorithms for finding the minimum weight triangulation of a simple polygon with (n− k) vertices on the perimeter and k vertice...
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We propose to look at the computational complexity of 2-dimensional geometric optimization problems on a finite point set with respect to the number of inner points (that is, points in the interior of the convex hull). As a case study, we consider the minimum weight triangulation problem. Finding a minimum weight triangulation for a set of n points in the plane is not known to be NP-hard nor so...
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We show that the length of the minimum weight Steiner triangulation (MWST) of a point set can be approximated within a constant factor by a triangulation algorithm based on quadtrees. In O(n log n) time we can compute a triangulation with O(n) new points, and no obtuse triangles, that approximates the MWST. We can also approximate the MWST with triangulations having no sharp angles. We generali...
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Minimum Weight Triangulation problem (MWT) is to nd a set of edges of minimum total length that triangulates a given set of points in the plane. Although some properties of MWT have been proved and many heuristics proposed, polyno-miality (and)/or NP-completness of MWT problem is still unsolved. The problem belongs to the few open problems from the book GaJo]. In this paper we present results i...
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ژورنال
عنوان ژورنال: Computational Geometry
سال: 1993
ISSN: 0925-7721
DOI: 10.1016/0925-7721(93)90016-y