Searching a Polygonal Region by a Boundary Searcher

  • Xue-Hou Tan
  • Published 2009 in Journal of Computer Science and Technology

Abstract

This paper considers the problem of planning the motion of a searcher in a polygonal region to eventually “see” an intruder that is unpredictable and capable of moving arbitrarily fast. A searcher is called the boundary searcher if he continuously moves on the polygon boundary and can see only along the rays of the flashlights he holds at a time. We present necessary and sufficient conditions for an n-sided polygon to be searchable by a boundary searcher. Based on our characterization, the equivalence of the ability of the searchers having only one flashlight and the one of the searchers having full 360° vision is simply established, and moreover, an optimal O(n) time and space algorithm for determining the searchability of simple polygons is obtained. We also give an O(n log n + I) time algorithm for generating a search schedule if it exists, where I (<3n 2) is the number of search instructions reported. Our results improve upon the previously known O(n 2) time and space bounds.

DOI: 10.1007/s11390-009-9241-4

Cite this paper

@article{Tan2009SearchingAP, title={Searching a Polygonal Region by a Boundary Searcher}, author={Xue-Hou Tan}, journal={Journal of Computer Science and Technology}, year={2009}, volume={24}, pages={505-516} }