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Searching a Polygonal Region by a Boundary Searcher

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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.

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Authors and Affiliations

  1. School of High-Technology for Human Welfare, Tokai University, 317 Nishino, Numazu, 410-0395, Japan

    Xue-Hou Tan

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  1. Xue-Hou Tan
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Correspondence to Xue-Hou Tan.

Additional information

Some preliminary results of this paper were presented at IJCCGGT2003 [8].

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Tan, XH. Searching a Polygonal Region by a Boundary Searcher. J. Comput. Sci. Technol. 24, 505–516 (2009). https://doi.org/10.1007/s11390-009-9241-4

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  • DOI: https://doi.org/10.1007/s11390-009-9241-4

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