Quasi-greedy triangulations approximating the minimum weight triangulation
Journal of Algorithms
Minimum convex partition of a constrained point set
Discrete Applied Mathematics - Special issue 14th European workshop on computational geometry CG'98 Selected papers
A combinatorial approach to planar non-colliding robot arm motion planning
FOCS '00 Proceedings of the 41st Annual Symposium on Foundations of Computer Science
Allocating Vertex π-Guards in Simple Polygons via Pseudo-Triangulations
Discrete & Computational Geometry
Enumerating pseudo-triangulations in the plane
Computational Geometry: Theory and Applications
Minimum weight triangulation is NP-hard
Proceedings of the twenty-second annual symposium on Computational geometry
Minimum weight pseudo-triangulations
Computational Geometry: Theory and Applications
Decompositions, Partitions, and Coverings with Convex Polygons and Pseudo-Triangles
Graphs and Combinatorics
Approximation algorithms for the minimum convex partition problem
SWAT'06 Proceedings of the 10th Scandinavian conference on Algorithm Theory
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In this paper we consider the problem of decomposing a simple polygon into subpolygons that exclusively use vertices of the given polygon. We allow two types of subpolygons: pseudo-triangles and convex polygons. We call the resulting decomposition PT-convex. We are interested in minimum decompositions, i.e., in decomposing the input polygon into the least number of subpolygons. Allowing subpolygons of one of two types has the potential to reduce the complexity of the resulting decomposition considerably. The problem of decomposing a simple polygon into the least number of convex polygons has been considered. We extend a dynamic-programming algorithm of Keil and Snoeyink for that problem to the case that both convex polygons and pseudo-triangles are allowed. Our algorithm determines such a decomposition in O(n^3) time and space, where n is the number of the vertices of the polygon.