# 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.

## Keywords

Competitive Ratio Simple Polygon Polygonal Chain Reflex Vertex Visibility Polygon## Preview

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