Position-independent street searching

Abstract

A polygon P is a street if there exist points (u,v) on the boundary such that P is weakly visible from any path from u to v. Optimal strategies have been found for on-line searching of streets provided that the starting position of the robot is s = u and the target is located at t = v. Thus a hiding target could foil the strategy of the robot by choosing its position t in such a manner as not to realize a street. In this paper we introduce a strategy with a constant competitive ratio to search a street polygon for a target located at an arbitrary point t on the boundary, starting at any other arbitrary point s on the boundary. We also provide lower bounds for this problem. This makes streets only the second non-trivial class of polygons (after stars) known to admit a constant-competitive-ratio strategy in the general position case.