The Two Guards Problem

Given a simple polygon in the plane with two distinguished vertices, s and g, is it possible for two guards to simultaneously walk along the two boundary chains from s to g in such a way that they are always mutually visible? We decide this question in time O(n log n) and in linear space, where n is the number of edges of the polygon. Moreover, we compute a walk of minimum length within time O(n log n + k), where k is the size of the output, and we prove that this is optimal.

• Type: Conference
• Year: 1991
• Where: COMPGEOM
• Authors: Christian Icking, Rolf Klein
• Keywords: Boundary Chains, COMPGEOM 1991, Discrete Geometry, Distinguished Vertices, Simple Polygon