Computing the rectilinear link diameter of a polygon
The problem of finding the diameter of a simple polygon has been studied extensively in recent years. O(n log n) time upper bounds have been given for computing the geodesic diameter and the link diameter for a polygon.
We consider the rectilinear case of this problem and give a linear time algorithm to compute the rectilinear link diameter of a simple rectilinear polygon. To our knowledge this is the first optimal algorithm for the diameter problem of non-trivial classes of polygons.
Unable to display preview. Download preview PDF.
- [B89]Mark De Berg. On Rectilinear Link Distance. Technical Report RUU-CS-89-13, Department of Computer Science, University of Utrecht, P.O.Box 80.089, 3502 TB Utrecht, the Netherlands, May 1989.Google Scholar
- [BKNO90]M.T. de Berg, M.J. van Kreveld, B.J. Nilsson, M.H. Overmars. Finding Shortest Paths in the Presence of Orthogonal Obstacles Using a Combined L 1 and Link Metric. In Proc. 2nd Scandinavian Workshop on Algorithm Theory, pages 213–224, 1990.Google Scholar
- [Cha90]Bernard Chazelle. Triangulating a Simple Polygon in Linear Time. In Proc. 31th Symposium on Foundations of Computer Science, pages 220–230, 1990.Google Scholar
- [Ke89]Yan Ke. An Efficient Algorithm for Link-distance Problems. In Proceedings of the Fifth Annual Symposium on Computational Geometry, pages 69–78, ACM, ACM Press, Saarbrücken, West Germany, June 1989.Google Scholar
- [Lev87]Christos Levcopoulos. Heuristics for Minimum Decompositions of Polygons. PhD thesis, University of Linköping, Linköping, Sweden, 1987.Google Scholar
- [NS91]B.J. Nilsson, S. Schuierer. An Optimal Algorithm for the Rectilinear Link Center of a Rectilinear Polygon. In 2nd Workshop on Algorithms and Data Structures, Lecture Notes in Computer Science, 1991.Google Scholar
- [Sur87]Subhash Suri. Minimum Link Paths in Polygons and Related Problems. PhD thesis, Johns Hopkins University, Baltimore, Maryland, August 1987. pages 213–224, 1990.Google Scholar