Position-independent near optimal searching and on-line recognition in star polygons

Abstract

We study the problem of on-line searching for a target inside a polygon. In particular we propose a strategy for finding a target of unknown location in a star polygon with a competitive ratio of 14.5, and we further refine it to 12.72. This makes star polygons the first non-trivial class of polygons known to admit constant competitive searches independent of the position of the target. We also provide a lower bound of 9 for the competitive ratio of searching in a star polygon-which is dose to the upper bound. A similar task consists of the problem of on-line recognition of star polygons for which we also present a strategy with a constant competitive ratio including negative instances.