# A Characterization of Polygonal Regions Searchable from the Boundary

## Abstract

We consider the problem of searching for a moving target with unbounded speed in a dark polygonal region by a searcher. The searcher continuously moves on the polygon boundary and can see only along the rays of the flashlights emanating from his position at a time. We present necessary and sufficient conditions for a polygon of *n* vertices to be *searchable from the boundary*. Our two main results are the following:

- 1
We present an

*O*(*n*log*n*) time and*O*(*n*) space algorithm for testing the searchability of simple polygons. Moreover, a search schedule can be reported in time linear in its size*I*, if it exists. For the searcher having full 360° vision,*I*< 2*n*, and for the searcher having only one flashlight,*I*< 3*n*^{2}. Our result improves upon the previous*O*(*n*^{2}) time and space solution, given by LaValle et al [5]. Also, the linear bound for the searcher having full 360° vision solves an open problem posed by Suzuki et al [7]. - 2
We show the equivalence of the abilities of the searcher having only one flashlight and the one having full 360° vision. Although the same result has been obtained by Suzuki et al [7], their proof is long and complicated, due to lack of the characterization of boundary search.

## Keywords

Boundary Point Simple Polygon Minimum Vertex Corner Incident Polygonal Region## Preview

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## References

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