A new data structure for shortest path queries in a simple polygon
Information Processing Letters
Triangulating a simple polygon in linear time
Discrete & Computational Geometry
A pedestrian approach to ray shooting: shoot a ray, take a walk
SODA '93 Selected papers from the fourth annual ACM SIAM symposium on Discrete algorithms
Drawing outerplanar minimum weight triangulations
Information Processing Letters
Pseudo-triangulations: theory and applications
Proceedings of the twelfth annual symposium on Computational geometry
Minimal tangent visibility graphs
Computational Geometry: Theory and Applications
Computational geometry: algorithms and applications
Computational geometry: algorithms and applications
Quasi-greedy triangulations approximating the minimum weight triangulation
Journal of Algorithms
Kinetic collision detection for simple polygons
Proceedings of the sixteenth annual symposium on Computational geometry
Kinetic maintenance of context-sensitive hierarchical representations for disjoint simple polygons
Proceedings of the eighteenth annual symposium on Computational geometry
Allocating vertex π-guards in simple polygons via pseudo-triangulations
SODA '03 Proceedings of the fourteenth annual ACM-SIAM symposium on Discrete algorithms
Which Triangulations Approximate the Complete Graph?
Proceedings of the International Symposium on Optimal Algorithms
A combinatorial approach to planar non-colliding robot arm motion planning
FOCS '00 Proceedings of the 41st Annual Symposium on Foundations of Computer Science
Minimum weight triangulation is NP-hard
Proceedings of the twenty-second annual symposium on Computational geometry
On constrained minimum pseudotriangulations
COCOON'03 Proceedings of the 9th annual international conference on Computing and combinatorics
Decomposing a simple polygon into pseudo-triangles and convex polygons
Computational Geometry: Theory and Applications
A quasi-polynomial time approximation scheme for minimum weight triangulation
Journal of the ACM (JACM)
On minimum weight pseudo-triangulations
Computational Geometry: Theory and Applications
Empty pseudo-triangles in point sets
Discrete Applied Mathematics
Fundamenta Informaticae - Emergent Computing
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We consider the problem of computing a minimum weight pseudo-triangulation of a set of n points in the plane. We first present an -time algorithm that produces a pseudo-triangulation of weight which is shown to be asymptotically worst-case optimal, i.e., there exists a point set for which every pseudo-triangulation has weight , where is the weight of a minimum weight spanning tree of . We also present a constant factor approximation algorithm running in cubic time. In the process we give an algorithm that produces a minimum weight pseudo-triangulation of a simple polygon.