Alon Efrat, Leonidas J. Guibas, Sariel Har-Peled, David C. Lin, Joseph S. B. Mitchell, and T. M. Murali. Sweeping simple polygons with a chain of guards. In Symposium on Discrete Algorithms, pages 927--936, 2000. (a) (b) (c) (d) (e) (f)  Home/Search   Document Details and Download   Summary   Related Articles   Check

....polynomial solutions for the cases of single 2 searcher and single # searcher. Independently of [1] Icking and Klein [7] defined the two guard walkability problem , which is a search problem for two guards who move on the boundary of a polygon while maintaining mutual visibility. Efrat et al. [10] considered a generalization: pursuit evasion by a chain of k guards, subject to the restriction that the first and the k th guards always move on the boundary while guard i, 1 i k moves in the interior of the polygon and maintains visibility with her neighbors, guards i 1 and i 1. Efrat ....

....a generalization: pursuit evasion by a chain of k guards, subject to the restriction that the first and the k th guards always move on the boundary while guard i, 1 i k moves in the interior of the polygon and maintains visibility with her neighbors, guards i 1 and i 1. Efrat et al. [10] gave a polynomial algorithm for the k guards problem. Note that the pursuit with two 1 searchers is 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 ....

A. Efrat, L. J. Guibas, S. Har-Peled, D. C. Lin, J. S. B. Mitchell, and T. M. Murali, "Sweeping simple polygons with a chain of guards," in Proc. ACM-SIAM SoDA, 2000, pp. 927--936.

....n n) algorithm which, given a polygon with n edges and m concave regions, decides whether the polygon is searchable and if so, constructs a schedule for the 1 searcher. Section 5 discusses an implementation of the algorithm, and also the relationship between our result and the results in Refs. [3,5,7,10,13]. Section 6 concludes the paper with a summary and directions for future research. 2. Notation and Preliminaries 2.1. Visibility and Con gurations Let P be a simple polygon. From now on, a polygon is always assumed to be simple. We denote the boundary of P by P . We assume that P P and ....

A. Efrat, L. J. Guibas, S. Har-Peled, D. C. Lin, J. S. B. Mitchell, and T. M. Murali. Sweeping simple polygons with a chain of guards. In Proceedings, ACM-SIAM Symposium on Discrete Algorithms (SODA), pages 927-936, San Francisco, CA, USA, 2000.

....number of pursuers needed to clear a polygonal region with holes is NP hard. Recently, Park et al. 13] gave 3 necessary and sufficient conditions for a polygon to be searchable and showed that there is an O(n time algorithm for constructing a search path for an n sided polygon. Efrat et al. [4] gave a polynomial time algorithm for the problem of clearing a simple polygon with a chain of k pursuers when the first and last pursuer have to move on the boundary of the polygon. 1.3 New Results We present a hunter strategy for general networks that improves significantly on the results ....

A. Efrat, L. J. Guibas, S. Har-Peled, D. C. Lin, J. S. B. Mitchell, and T. M. Murali. Sweeping simple polygons with a chain of guards. In Proceedings of the 11th ACM-SIAM Symposium on Discrete Algorithms (SODA), pages 927--936, 2000.

.... 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] ....

A. Efrat, L. Guibas, S. Har-Peled, D. Lin, J. Mitchell, and T. Murali. Sweeping simple polygons with a chain of guards. In Proc. of 16th Symp. on Discrete Algorithm, pages 927--936, 2000.

....for the case of omnidirectional visibility was rst presented in [10] Solutions to the case in which the pursuer has one or more detection beams are considered in [4, 11, 16, 18, 19] for various types of polygons. A pursuit evasion algorithm for curved environments was presented in [9] In [5], both optimal and approximation algorithms were presented for the case of a chain of pursuers that maintain mutual pairwise visibility in a polygonal environment. Until very recently [18] it has been unknown whether the omnidirectional pursuit evasion problem in a polygonal environment could ....

A. Efrat, L. J. Guibas, D. C. Lin, J. S. B. Mitchell, and T. M. Murali. Sweeping simple polygons with a chain of guards. In Proc. ACM-SIAM Sympos. Discrete Algorithms, 2000.

....3.3 we present an O(n 2 ) algorithm which, given a polygon with n edges, decides whether the polygon is 1 searchable and if so, outputs a schedule for the pursuer. Section 4 discusses an implementation of the algorithm, and also the relationship between our result and the results in [7, 5, 12] [3] and [9] Section 5 concludes the paper with a summary and directions for future research. 2. NOTATION AND PRELIMINARIES 2.1 Notation Let P be a simple polygon. From now on, a polygon is always assumed to be simple. We denote the boundary of P by P . We assume that P P and that P is ....

....of the polygons that can be cleared by two guards. Also, note that while the polygon 6 (a) b) c) d) e) f) g) h) Figure 5: A polygon which requires recontamination (between frames (d) and (e) in Figure 5 can be cleared by a chain of three guards using an algorithm by Efrat et al. [3] (this is generalization of the two guards problem to a chain of k guards) this is not equivalent to nding a solution for a 1 searcher. Similarly, it is not hard to show that every point in the polygon in Figure 5 is contaminated at some time during any successful 1 searcher schedule. Thus ....

A. Efrat, L. J. Guibas, S. Har-Peled, D. C. Lin, J. S. B. Mitchell, and T. M. Murali. Sweeping simple polygons with a chain of guards. In Proceedings, ACM-SIAM Symposium on Discrete Algorithms (SODA), 2000. to appear.

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A. Efrat, L. J. Guibas, S. Har-Peled, D. C. Lin, J. S. B. Mitchell, and T. M. Murali. Sweeping simple polygons with a chain of guards. In Symposium on Discrete Algorithms, pages 927-936, 2000.

....that lies inside the polygon. The morphing width of two polylines is a metric. It is a new method of computing the similarity between two polylines. One interesting by product of our algorithms is a solution to the following problem, other variants of which have been considered in the literature [7, 16]: Sweep a polygon with a chain of guards such that a target moving continuously inside the polygon is discovered. Our techniques ensure that we can minimise the length of the chain of the guards (or approximate the minimum length) while ensuring that each point in the polygon is swept over only ....

A. Efrat, L. J. Guibas, S. Har-Peled, D. C. Lin, J. S. B. Mitchell, and T. M. Murali. Sweeping simple polygons with a chain of guards. In Proc. 11th ACM-SIAM Symposium on Discrete Algorithms, pages 927--936, 2000.

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Alon Efrat, Leonidas J. Guibas, Sariel Har-Peled, David C. Lin, Joseph S. B. Mitchell, and T. M. Murali. Sweeping simple polygons with a chain of guards. In Symposium on Discrete Algorithms, pages 927--936, 2000. (a) (b) (c) (d) (e) (f)

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A. Efrat, L. J. Guibas, S. Har-Peled, D. C. Lin, J. S. B. Mitchell, and T. M. Murali. Sweeping simple polygons with a chain of guards. In Proceedings, ACM-SIAM Symposium on Discrete Algorithms (SODA), 2000. to appear.

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A. Efrat, L. J. Guibas, S. Har-Peled, D. C. Lin, J. S. B. Mitchell, and T. M. Murali, \Sweeping simple polygons with a chain of guards," in Proceedings, ACM-SIAM Symposium on Discrete Algorithms (SODA), San Francisco, CA, USA, 2000, pp. 927-936.

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A. Efrat, L. J. Guibas, S. Har-Peled, D. C. Lin, J. S. B. Mitchell, and T. M. Murali, "Sweeping simple polygons with a chain of guards," in Proceedings of the Symposium on Discrete Algorithms, January 2000.

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A. Efrat, L. J. Guibas, D. C. Lin, J. S. B. Mitchell, and T. M. Murali. Sweeping simple polygons with a chain of guards. In Proc. ACM-SIAM Sympos. Discrete Algorithms, 2000.

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A. Efrat, L. J. Guibas, S. Har-Peled, D. C. Lin, J. S. B. Mitchell, and T. M. Murali. Sweeping simple polygons with a chain of guards. In Proceedings of the 11th ACM-SIAM Symposium on Discrete Algorithms (SODA), pages 927--936, 2000.

No context found.

Alon Efrat, Leonidas J. Guibas, Sariel Har-Peled, David C. Lin, Joseph S. B. Mitchell, and T. M. Murali. Sweeping simple polygons with a chain of guards. In Proceedings, ACM-SIAM Symposium on Discrete Algorithms (SODA), pages 927--936, San Francisco, CA, USA, 2000.

No context found.

A. Efrat, L. J. Guibas, S. Har-Peled, D. C. Lin, J. S. Mitchell, and T. M. Murali. Sweeping simple polygons with a chain of guards. In Proc. 11th ACM-SIAM Sympos. Discrete Algorithms (SODA'2000) (2000) 927--936.

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A. Efrat, L. J. Guibas, S. Har-Peled, D. C. Lin, J. S. B. Mitchell, and T. M. Murali. Sweeping simple polygons with a chain of guards. In Proceedings, ACM-SIAM Symposium on Discrete Algorithms (SODA), 2000. to appear.

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