arXiv subjects

Eunjin Oh

Publications and source records attributed to Eunjin Oh.

39 records · Page 3Linked to original sources

arXiv2018

Voronoi Diagrams for a Moderate-Sized Point-Set in a Simple Polygon

Given a set of sites in a simple polygon, a geodesic Voronoi diagram of the sites partitions the polygon into regions based on distances to sites under the geodesic metric. We present algorithms for computing the geodesic nearest-point, higher-order and farthest-point Voronoi diagrams of m point sites in a simple n-gon, which improve the best known ones for m <= n/ polylog n. Moreover, the algorithms for the geodesic nearest-point and farthest-point Voronoi diagrams are optimal for m <= n/ polylog n. This partially answers a question posed by Mitchell in the Handbook of Computational Geometry.

cs.CG↗

arXiv2017

The Geodesic $2$-center Problem in a Simple Polygon

The geodesic $k$-center problem in a simple polygon with $n$ vertices consists in the following. Find a set $S$ of $k$ points in the polygon that minimizes the maximum geodesic distance from any point of the polygon to its closest point in $S$. In this paper, we focus on the case where $k=2$ and present an exact algorithm that returns a geodesic $2$-center in $O(n^2\log^2 n)$ time.

cs.CG↗

arXiv2015

A linear-time algorithm for the geodesic center of a simple polygon

Given two points in a simple polygon $P$ of $n$ vertices, its geodesic distance is the length of the shortest path that connects them among all paths that stay within $P$. The geodesic center of $P$ is the unique point in $P$ that minimizes the largest geodesic distance to all other points of $P$. In 1989, Pollack, Sharir and Rote [Disc. \& Comput. Geom. 89] showed an $O(n\log n)$-time algorithm that computes the geodesic center of $P$. Since then, a longstanding question has been whether this running time can be improved (explicitly posed by Mitchell [Handbook of Computational Geometry, 2000]). In this paper we affirmatively answer this question and present a linear time algorithm to solve this problem.

cs.CG↗