Online exploration outside a convex obstacle

TL;DR

This paper introduces an online algorithm for exploring the area outside an unknown convex polygon, achieving a competitive ratio of approximately 22.77 compared to the optimal offline solution.

Contribution

It presents the first online exploration algorithm for the outside of an unknown convex polygon with a proven competitive ratio.

Findings

Algorithm guarantees a ~22.77 competitive ratio

First online solution for exploring outside unknown convex polygons

Provides theoretical bounds for exploration efficiency

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 $\mathbb{R}^2\setminus \Omega$, where $\Omega$ 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 algorithms guarantees a $\approx 22.77$ competitive ratio compared to the optimal offline watchman path.