THE TWO GUARDS PROBLEM

CHRISTIAN ICKING, ROLF KLEIN
1992 International journal of computational geometry and applications  
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.
doi:10.1142/s0218195992000160 fatcat:phmadhsjpfe7bl72k4rcatjdvi