Minimum-Link Paths Among Obstacles in the Plane

Given a set of nonintersecting polygonal obstacles in the plane, the link distance between two points s and t is the minimum number of edges required to form a polygonal path connecting s to t that avoids all obstacles. We present an algorithm that computes the link distance and a corresponding minimum-link path between two points in time OEnlog2 n and space OE, where n is the total number of edges of the obstacles, E is the size of the visibility graph, and n denotes the extremely slowly growing inverse of Ackermann's function. We show how to extend our method to allow computation of a tree rooted at s of minimum-link paths from s to all obstacle vertices. This leads to a method of solving the query version of our problem for query points t.

• Type: Conference
• Year: 1990
• Where: COMPGEOM
• Authors: Joseph S. B. Mitchell, Günter Rote, Gerhard J. Woeginger
• Keywords: COMPGEOM 1990, Discrete Geometry, Link Distance, Minimum-link Paths, Nonintersecting Polygonal Obstacles