A heuristic triangulation algorithm
Journal of Algorithms
Pseudo-triangulations: theory and applications
Proceedings of the twelfth annual symposium on Computational geometry
Quasi-greedy triangulations approximating the minimum weight triangulation
Journal of Algorithms
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
Spatial embedding of pseudo-triangulations
Proceedings of the nineteenth annual symposium on Computational geometry
A combinatorial approach to planar non-colliding robot arm motion planning
FOCS '00 Proceedings of the 41st Annual Symposium on Foundations of Computer Science
On constrained minimum pseudotriangulations
COCOON'03 Proceedings of the 9th annual international conference on Computing and combinatorics
| Hi-index | 0.00 |
We consider the problem of computing a minimum weight pseudo-triangulation of a set ${\mathcal S}$ of n points in the plane. We first present an $\mathcal O(n {\rm log} n)$-time algorithm that produces a pseudo-triangulation of weight $O(wt(\mathcal M(\mathcal S)).{\rm log} n)$ which is shown to be asymptotically worst-case optimal, i.e., there exists a point set ${\mathcal S}$ for which every pseudo-triangulation has weight $\Omega({\rm log} n.wt(\mathcal M(\mathcal S))$, where $wt(\mathcal M(\mathcal S))$ is the weight of a minimum spanning tree of ${\mathcal S}$. 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.