Online exploration outside a convex obstacle

Abstract

A watchman path is a path such that a direct line of sight exists between each point in some region and some point along the path. Here, we study the online watchman path problem outside a convex polygon, i.e., in R2∖Ω, where Ω is a convex polygon that is not known in advance. We present an algorithm for the exploration of the region outside the polygon. We prove that the presented algorithm guarantees a ≈50.2072 competitive ratio compared to the optimal offline watchman path.