Online Vertex Exploration Problems in a Simple Polygon

Abstract

This paper considers online vertex exploration problems in a simple polygon where starting from a point in the inside of a simple polygon, a searcher is required to explore a simple polygon to visit all its vertices and finally return to the initial position as quickly as possible. The information of the polygon is given online. As the exploration proceeds, the searcher gains more information of the polygon. We give a 1.219-competitive algorithm for this problem. We also study the case of a rectilinear simple polygon, and give a 1.167-competitive algorithm.