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 matt...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.展开更多
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 boun...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.展开更多
基金supported by the Grand-in-Aid of the Ministry of Education, Science, Sports and Culture of Japan, and a research grant from Tokai University.
文摘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.
文摘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.
