IJCCGGT 2003: Combinatorial Geometry and Graph Theory pp 200-215

# A Characterization of Polygonal Regions Searchable from the Boundary

• Xuehou Tan
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3330)

## 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. 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 < 2n, 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. 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
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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