Polynomial-time instances of the minimum weight triangulation problem
Computational Geometry: Theory and Applications
Computing a subgraph of the minimum weight triangulation
Computational Geometry: Theory and Applications
A (usually?) connected subgraph of the minimum weight triangulation
Proceedings of the twelfth annual symposium on Computational geometry
On computing edges that are in all minimum-weight triangulations
Proceedings of the twelfth annual symposium on Computational geometry
Quasi-greedy triangulations approximating the minimum weight triangulation
Journal of Algorithms
SCG '99 Proceedings of the fifteenth annual symposium on Computational geometry
Maximum weight triangulation and graph drawing
Information Processing Letters
A lower bound for &bgr;-skeleton belonging to minimum weight triangulations
Computational Geometry: Theory and Applications
On ß-skeleton as a subgraph of the minimum weight triangulation
Theoretical Computer Science
A Branch-and-Cut Approach for Minimum Weight Triangulation
ISAAC '97 Proceedings of the 8th International Symposium on Algorithms and Computation
ISAAC '96 Proceedings of the 7th International Symposium on Algorithms and Computation
The traveling salesman problem with few inner points
Operations Research Letters
Parameterized Complexity
Minimum-weight triangulation is NP-hard
Journal of the ACM (JACM)
A fixed parameter algorithm for optimal convex partitions
Journal of Discrete Algorithms
Hi-index | 0.00 |
We 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 solvable in polynomial time, but when the points are in convex position, the problem can be solved in O(n3) time by dynamic programming. We extend the dynamic programming approach to the general problem and describe an exact algorithm which runs in O(6kn5 logn) time where n is the total number of input points and k is the number of inner points. If k is taken as a parameter, this is a fixed-parameter algorithm. It also shows that the problem can be solved in polynomial time if k = O(log n). In fact, the algorithm works not only for convex polygons, but also for simple polygons with k inner points.