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Searching a Polygonal Region by Two Guards

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Abstract

We study the problem of searching for a mobile intruder in a polygonal region P by two guards. The objective is to decide whether there should exist a search schedule for the two guards to detect the intruder, no matter how fast the intruder moves, and if so, generate a search schedule. During the search, the two guards are required to walk on the boundary of P continuously and be mutually visible all the time. We present a characterization of the class of polygons searchable by two guards in terms of non-redundant components, and thus solve a long-standing open problem in computational geometry. Also, we give an optimal O(n) time algorithm to determine the two-guard searchability in a polygon, and an O(n log n + m) time algorithm to generate a search schedule, if it exists, where n is the number of vertices of P and m (≤ n 2) is the number of search instructions reported.

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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

  2. School of Information Science and Technology, Dalian Maritime University, Dalian, 116026, China

    Xue-Hou Tan & Bo Jiang

Authors
  1. Xue-Hou Tan
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  2. Bo Jiang
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Correspondence to Xue-Hou Tan.

Additional information

This research is partially supported by the Grand-in-Aid of the Ministry of Education, Science, Sports and Culture of Japan, and a research grant from Tokai University.

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Tan, XH., Jiang, B. Searching a Polygonal Region by Two Guards. J. Comput. Sci. Technol. 23, 728–739 (2008). https://doi.org/10.1007/s11390-008-9179-y

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  • DOI: https://doi.org/10.1007/s11390-008-9179-y

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