eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2019-06-11
12:1
12:14
10.4230/LIPIcs.SoCG.2019.12
article
Optimal Algorithm for Geodesic Farthest-Point Voronoi Diagrams
Barba, Luis
1
Department of Computer Science, ETH Zürich, Switzerland
Let P be a simple polygon with n vertices. For any two points in P, the geodesic distance between them is the length of the shortest path that connects them among all paths contained in P. Given a set S of m sites being a subset of the vertices of P, we present the first randomized algorithm to compute the geodesic farthest-point Voronoi diagram of S in P running in expected O(n + m) time. That is, a partition of P into cells, at most one cell per site, such that every point in a cell has the same farthest site with respect to the geodesic distance. This algorithm can be extended to run in expected O(n + m log m) time when S is an arbitrary set of m sites contained in P.
https://drops.dagstuhl.de/storage/00lipics/lipics-vol129-socg2019/LIPIcs.SoCG.2019.12/LIPIcs.SoCG.2019.12.pdf
Geodesic distance
simple polygons
farthest-point Voronoi diagram