Abstract
We study the problem of searching for a mobile intruder in a polygonal room P with a door d by a mobile searcher. The objective is to decide whether there exists a search schedule to detect the intruder without allowing him to evict through d, no matter how fast he moves, and if so, generate a search schedule. A searcher is called the k-searcher if he holds k flashlights and can see only along k rays emanating from his flashlights. The intruder is detected if he is ever illuminated by a flashlight. For a 1-searcher, we present an optimal O(n log n+m) time and O(n) space algorithm for generating a search schedule, if it exists, where n is the number of vertices of P and m (≤ n2) is the minimum number of search instructions required to clear P. This improves upon the previous O(n 2) time and space bounds. The optimality of our algorithm is obtained by identifying critical visibility events occurred in P and decomposing the search schedule based on them. Furthermore, our method can easily be extended to solve the problem of searching a room by a 2-searcher. The extension is based on a generalization of the notion of visibility to that of link-2-visibility.
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Tan, X. (2001). Efficient Algorithms for Searching a Polygonal Room with a Door. In: Akiyama, J., Kano, M., Urabe, M. (eds) Discrete and Computational Geometry. JCDCG 2000. Lecture Notes in Computer Science, vol 2098. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-47738-1_32
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DOI: https://doi.org/10.1007/3-540-47738-1_32
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