Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
414265 | Computational Geometry | 2015 | 11 Pages |
Abstract
In this paper, we show that the L1L1 geodesic diameter and center of a simple polygon can be computed in linear time. For the purpose, we focus on revealing basic geometric properties of the L1L1 geodesic balls, that is, the metric balls with respect to the L1L1 geodesic distance. More specifically, in this paper we show that any family of L1L1 geodesic balls in any simple polygon has Helly number two, and the L1L1 geodesic center consists of midpoints of shortest paths between diametral pairs. These properties are crucial for our linear-time algorithms, and do not hold for the Euclidean case.
Keywords
Related Topics
Physical Sciences and Engineering
Computer Science
Computational Theory and Mathematics
Authors
Sang Won Bae, Matias Korman, Yoshio Okamoto, Haitao Wang,