Document Type
Conference Paper
Journal/Book Title/Conference
24th Annual European Symposium on Algorithms (ESA 2016)
Volume
57
Publisher
Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing
Location
Aarhus, Denmark
Publication Date
8-22-2016
First Page
77:1
Last Page
77:17
Abstract
In this paper, we study the problem of computing Euclidean geodesic centers of a polygonal domain P of n vertices. We give a necessary condition for a point being a geodesic center. We show that there is at most one geodesic center among all points of P that have topologically-equivalent shortest path maps. This implies that the total number of geodesic centers is bounded by the size of the shortest path map equivalence decomposition of P, which is known to be O(n^{10}). One key observation is a pi-range property on shortest path lengths when points are moving. With these observations, we propose an algorithm that computes all geodesic centers in O(n^{11}*log(n)) time. Previously, an algorithm of O(n^{12+epsilon}) time was known for this problem, for any epsilon > 0.
Recommended Citation
Wang, H. On the geodesic centers of polygonal domains (2016) Leibniz International Proceedings in Informatics, LIPIcs, 57, art. no. 77, .
Included in
Discrete Mathematics and Combinatorics Commons, Numerical Analysis and Scientific Computing Commons, Theory and Algorithms Commons
Comments
http://drops.dagstuhl.de/opus/volltexte/2016/6418/