I. Suzuki, Y. Tazoe, M. Yamashita, and T. Kameda. Searching a polygonal region from the boundary. International Journal on Computational Geometry and Applications, 11(5):529--553, 2001.  Home/Search   Document Details and Download   Summary   Related Articles   Check

....not a special case of the k guards pursuit since (i) the 1 searchers are not required to maintain visibility all the time, and (ii) for each 1 searcher, the endpoint of the ray of light emitted by her flashlight does not have to move continuously along the boundary of the polygon. Suzuki et al. [STYK01] provided a polynomial time solution for a version of the pursuit in which a single is restricted to the boundary of the polygonal region. Vidal et al. 02] addressed a version of the pursuit evasion problem that uses probabilistic models. 1.2 Notation and preliminaries In the rest of the ....

Ichiro Suzuki, Yuichi Tazoe, Masafumi Yamashita, and Tiko Kameda. Searching a polygonal region from the boundary. International Journal of Computational Geometry and Applications, 11(5):529--553, October 2001.

....They defined di#erent kinds of pursuers depending on the number of beams (flashlights) is equipped with, e.g. a 1 searcher has one flashlight, a k searcher has k flashlights, and an # searcher has 360 # vision. This naturally defines a pursuit evasion problem for each class of searchers. [1, 2, 3] presented polynomial solutions for deciding searchability of special classes of polygons, the general case single pursuer problem was open for quite a while. Recently, the authors provided a O(n ) solution for a single 1 searcher in a polygon [4] Park et al. [5] presented polynomial solutions ....

I. Suzuki, Y. Tazoe, M. Yamashita, and T. Kameda, "Searching a polygonal region from the boundary," Int. J. of Comput. Geom. & Applic., vol. 11, no. 5, pp. 529--553, 2001.

....is also complete for the searcher with 360 # visibility. There are some open problems: Is there any simple proof (without resorting to a characterization) to show that the 2 searcher and the searcher with 360 # visibility have the same search capability Some partial results can be found in [7, 14]. Extend the characterization in this paper to the case of multiple searchers where the searchers should form a chain during the search [2] For multiple searchers without chain restriction, the complexity of constructing a search schedule is in NP hard [3] ....

I. Suzuki, Y. Tazoe, M. Yamashita, and T. Kameda. Searching a polygonal region from the boundary. In TR-20000925, EECS Department, Univ. of Wisconsin-Milwaukee, 2000.

....with shadow. Interestingly, a special case of our proof shows that if the searcher is restricted to move along the boundary of the polygon throughout the search, the 1 searcher and the # searcher have the same search capability. The same result was independently shown by Suzuki et al. [8]. Their proof uses some topological arguments. Compared to their results, our approach is simple, shows the same result as [8] under the boundary restriction, and shows a much stronger result for the original conjecture. 2 Definitions and Notations Let #P denote the boundary of a simple polygon ....

....boundary of the polygon throughout the search, the 1 searcher and the # searcher have the same search capability. The same result was independently shown by Suzuki et al. 8] Their proof uses some topological arguments. Compared to their results, our approach is simple, shows the same result as [8] under the boundary restriction, and shows a much stronger result for the original conjecture. 2 Definitions and Notations Let #P denote the boundary of a simple polygon P . The searcher and intruder are modeled as points that move continuously within P . Let #(t) denote the position of the ....

I. Suzuki, Y. Tazoe, M. Yamashita, and T. Kameda. Searching a polygonal region from the boundary. In Technical Report TR-20000925, EECS Department, Univ. of Wisconsin-Milwaukee, 2000.

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I. Suzuki, Y. Tazoe, M. Yamashita, and T. Kameda. Searching a polygonal region from the boundary. International Journal on Computational Geometry and Applications, 11(5):529--553, 2001.

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