An optimal algorithm for the rectilinear link center of a rectilinear polygon
The problem of finding the center of an area has been studied extensively in recent years. O(nlogn) time upper bounds have been given for the link center and the geodesic center of a simple polygon.
We consider the rectilinear case of this problem, and give a linear time algorithm to compute the rectilinear link center of a simple rectilinear polygon. As a consequence we also obtain a linear time solution for the rectilinear link radius problem. To our knowledge this is the first optimal algorithm which solves a non-trivial center problem.
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 L1 and Link Metric. In Proc. 2nd Scandinavian Workshop on Algorithm Theory, Lecture Notes in Computer Science 447, 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
- [DLS89]H.N. Djidjev, A. Lingas, J.-R. Sack. An O(nlogn) Algorithm for Computing a Link Center in a Simple Polygon. In Proc. STACS, Lecture Notes in Computer Science 349, pages 96–107, 1989.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
- [LPS*87]W. Lenhart, R. Pollack, J.-R. Sack, R. Seidel, M. Sharir, S. Suri, G. Toussaint, S. Whitesides, C. Yap. Computing the Link Center of a Simple Polygon. In Proceedings of the Third Annual Symposium Computational Geometry, pages 1–10, ACM, ACM Press, Waterloo, Ontario, Canada, June 1987.Google Scholar
- [NS91]B.J. Nilsson, S. Schuierer. Computing the Rectilinear Link Diameter of a Polygon. In Proc. Workshop on Computational Geometry, CG91, Lecture Notes in Computer Science, 1991, To Appear.Google Scholar
- [Sur87]Subhash Suri. Minimum Link Paths in Polygons and Related Problems. PhD thesis, Johns Hopkins University, Baltimore, Maryland, August 1987.Google Scholar