Modern heuristic techniques for combinatorial problems
Rectilinear decompositions with low stabbing number
Information Processing Letters
Stabbing triangulations by lines in 3D
Proceedings of the eleventh annual symposium on Computational geometry
A (usually?) connected subgraph of the minimum weight triangulation
Proceedings of the twelfth annual symposium on Computational geometry
Implementations of the LMT heuristic for minimum weight triangulation
Proceedings of the fourteenth annual symposium on Computational geometry
ACM SIGACT News
Minimizing the stabbing number of matchings, trees, and triangulations
SODA '04 Proceedings of the fifteenth annual ACM-SIAM symposium on Discrete algorithms
Minimum-weight triangulation is NP-hard
Journal of the ACM (JACM)
Minimizing the Stabbing Number of Matchings, Trees, and Triangulations
Discrete & Computational Geometry
Orthogonal subdivisions with low stabbing numbers
WADS'05 Proceedings of the 9th international conference on Algorithms and Data Structures
| Hi-index | 0.00 |
The minimum stabbing triangulation of a set of points in the plane (mstr) was previously investigated in the literature. The complexity of the mstr remains open and, to our knowledge, no exact algorithm was proposed and no computational results were reported earlier in the literature of the problem. This paper presents integer programming (ip) formulations for the mstr, that allow us to solve it exactly through ip branch-and-bound (b&b) algorithms. Moreover, one of these models is the basis for the development of a sophisticated Lagrangian heuristic for the problem. Computational tests were conducted with two instance classes comparing the performance of the latter algorithm against that of a standard (exact) b&b. The results reveal that the Lagrangian algorithm yielded solutions with minute, and often null, duality gaps for instances with several hundreds of points in small computation times.