L. J. Guibas, J.-C. Latombe, S. M. LaValle, D. Lin, and R. Motwani, "A visibility-based pursuit-evasion problem," International Journal of Computational Geometry and Applications, vol. 9, no. 4/5, pp. 471--, 1999. [Online]. Available: citeseer.nj.nec.com/guibas96visibilitybased.html  Home/Search   Document Details and Download   Summary   Related Articles   Check

.... to guarantee, for each pair of points in the environment (say R and Gj, that the following expression is true: Gc,r r c V R (R (t) The problem seems very similar to coverage problems that have been deeply studied in the literature: art gallery problems [14] or the pursuit evasion problem [15]. However, neither of these approaches fits very well into the motivation of our research. First of all, we aim at designing cooperation strategies for robots that have a very limited knowledge (or no knowledge at all) of the environment and therefore rely on local navigation algorithms to find ....

L.J. Guibas, J.C. Latombe, S.M. LaValle, D. Lin, and R. Motwani, "A Visibility-Based Pursuit-Evasion Problem", International Journal of Computational Geometry & Applications, Vol. 9, Nos. 4 & 5 (1999) 471- 493.

....of guards needed to catch the fugitive is called the node search number of a graph [8] Pursuit evasion problems in the plane were introduced by Suzuki and Yamashita [16] They gave necessary and sufficient condition for a simple polygon to be searchable by a single pursuer. Later Guibas et al. [6] presented a complete algorithm and showed that the problem of determining the minimal 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 ....

L. J. Guibas, J.-C. Latombe, S. M. LaValle, D. Lin, and R. Motwani. A visibility-based pursuit-evasion problem. International Journal of Computational Geometry and Applications (IJCGA), 9(4):471--493, 1999.

....Multiple Model (VS IMM) estimator combined with an assignment algorithm for tracking multiple ground targets using multiple stationary sensors. As different approaches to the same problem [11, 12, 13] have studied the target tracking problem in the context of distributed immobile sensor networks. [14, 15] introduced the Pursuit Evasion problem, and analyzed the bounds on the number of necessary pursuers algorithmically. Several prior approaches [16, 17, 18, 19, 20] exist for the online construction of topological maps. We use the approach described in [17] 3 The Region based Approach Our ....

Leonidas J. Guibas, Jean-Claude Latombe, Steven M. LaValle, David Lin, and Rajeev Motwani, "A visibilitybased pursuit-evasion problem," International Journal of computational eometry and Applications, vol. 9, no. 5, pp. 471--494, October 1997.

....conditions for a polygon to be searchable by a searcher. Recently, LaValle et al. presented an O(n 2 ) time complete algorithm for constructing a search schedule of a 1 searcher for an n sided polygon. For a searcher with 360 vision, however, no polynomial time algorithm is known (refer to [2]) In this paper, we are interested in the characterization of the class of 1 searchable polygons. While an O(n 2 ) time complete algorithm is known, there are many reasons why this characterization is of interest. First, it is a theoretically interesting question, which looks very simple but ....

L.J. Guibas, J.C. Latombe, S.M. Lavalle, D. Lin, and R. Motwani. A visibility-based pursuit-evasion problem. Int. J. of Comp. Geom. and Appl., 9(4):471--493, 1999.

....placed at a fixed distance away from the boundary demarcating the two spaces. Such placement ensures that a receiver rarely makes a wrong choice, unless caught within a small distance from the boundary between two beacons advertising different spaces. In robotics, art gallery and pursuit evasion [8] problems have been well studied. In the art gallery analogy, the robot s goal is to move from one position to another to maximize visual coverage of its surroundings, as a human might try to do in a gallery. A complementary set of approaches addresses the pursuit evasion problem in which a ....

L. Guibas, , J. C. Latombe, S. M. LaValle, D. Lin, and R. Motwani. A visibility-based pursuit evasion problem. International Journal of Computational Geometry Applications, 9(5):471--494, October 1999.

.... the searchers and the intruder can move from vertex to vertex until a searcher and the intruder eventually lie in one vertex [11, 13] After adopting geometric free space constraints and visibility of the searchers, this problem has attracted much attention in computational geometry and robotics [1, 3 6, 8, 10, 15, 16, 18]. As the first attempt, Suzuki and Yamashita [15] introduced the polygon search problem, which is the topic of this paper. They presented some necessary or su#cient conditions for a polygon to be searchable by a single searcher but no complete characterizations. Guibas et al. 3] presented a ....

....8, 10, 15, 16, 18] As the first attempt, Suzuki and Yamashita [15] introduced the polygon search problem, which is the topic of this paper. They presented some necessary or su#cient conditions for a polygon to be searchable by a single searcher but no complete characterizations. Guibas et al. [3] presented a complete algorithm to search a polygon by a single searcher, but the complexity of this problem, including the analysis of their algorithm, remains open. As a characterizable variant of the polygon, many researchers considered rooms and corridors. A room is a polygonal region having ....

[Article contains additional citation context not shown here]

L.J. Guibas, J.C. Latombe, S.M. Lavalle, D. Lin, and R. Motwani. A visibility-based pursuit-evasion problem. Int. J. of Comp. Geom. and Appl., 9(4):471--493, 1998.

....main open problem raised in [9] is to find a simple characterization (or an efficient algorithm to compute a search schedule) of # searchable polygons. In spite of many researches, complete characterizations or efficient algorithms are known only for special cases of the polygon search problem [3, 1, 2, 5, 7]. Recently, LaValle et al. 4] presented an O(n 2 ) time complete algorithm for constructing a search schedule of the 1 searcher. Lee et al. 6] presented an O(n 2 ) time algorithm to find a search schedule of the 2 searcher. However, the characterization of the class of # searchable ....

L.J. Guibas, J.C. Latombe, S.M. Lavalle, D. Lin, and R. Motwani. A visibilitybased pursuit-evasion problem. Int. J. of Comp. Geom. and Appl., 9(4):471-- 493, 1998.

....model is available i.e. the probability density function p(#(t) is given then it is possible to compute a motion plan that is the best in the expected sense. In any event, the unpredictable case has to be solved on line. Unless there is a mechanism for re acquiring the target [12], a good tracker seeks to maximize t esc as opposed to maximize the exposure. A strategy designed for the worst case scenario will anticipate the target s most adverse action for a future horizon T , execute a small (possibly di#erential) initial portion of the computed strategy, and repeat the ....

L.J. Guibas, J.C. Latombe, S.M. Lavalle, D. Lin, and R.Motwani, "Visibility-based pursuit-evasion problem," Int. J. of Computational Geometry and Applications, vol. 9, no. 5, pp. 471--494, 1999.

....is identified for which a single pursuer suffices. We have derived several bounds on H(F ) over certain classes of free spaces. It can be shown that for any simply connected free space F with n edges, at worst H(F ) O(lgn) and for general free spaces with h holes, at worst H(F ) O(h lg n) [6]. To obtain the first result, F can be recursively decomposed by placing pursuers on partitioning edges to prevent the evader from moving from one portion of F to another. A logarithmic number of pursuers can be systematically swept across partition edges to obtain the solution strategy. To obtain ....

....to find an evader that can execute continuous motions along the edges of a graph. Instead of using visibility, capture is achieved when one of the pursuers touches the evader. We have shown that for any instance of Parsons problem on a planar graph, there exists an equivalent geometric instance [6]. The basic idea is to replace each edge in the graph by a thin corridor that has four bends. The key difference between the graph problem and the geometric problem is the power of visibility, which is essentially removed once four bend corridors are used. By transforming difficult graph instances ....

[Article contains additional citation context not shown here]

L. J. Guibas, J.-C. Latombe, S. M. LaValle, D. Lin, and R. Motwani. A visibility-based pursuit-evasion problem. 1996. Submitted to International Journal of Computational Geometry and Applications.

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L. J. Guibas, J.-C. Latombe, S. M. LaValle, D. Lin, and R. Motwani, "A visibility-based pursuit-evasion problem," International Journal of Computational Geometry and Applications, vol. 9, no. 4/5, pp. 471--, 1999. [Online]. Available: citeseer.nj.nec.com/guibas96visibilitybased.html

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L. J. Guibas, J. Latombe, S. M. LaValle, D. Lin, and R. Motwani, "A visibility-based pursuit-evasion problem," Int. J. Computat. Geometry Applicat., vol. 9, no. 5, pp. 471--494, 1999.

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L. J. Guibas, J. Latombe, S. M. LaValle, D. Lin, and R. Motwani, "A visibility-based pursuit-evasion problem," Int. J. Computat. Geometry Applicat., vol. 9, no. 5, pp. 471--494, 1999.

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L. J. Guibas, J.-C. Latombe, S. M. LaValle, D. Lin, and R. Motwani, "A visibility-based pursuit-evasion problem," International Journal of Computational Geometry and Applications, vol. 9, no. 4/5, pp. 471--, 1999. [Online]. Available: citeseer.nj.nec.com/guibas96visibilitybased.html

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L. J. Guibas, J.-C. Latombe, S. M. LaValle, D. Lin, and R. Motwani. A visibility-based pursuit-evasion problem. International Journal of Computational Geometry and Applications, 9(4/5):471--, 1999.

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L. J. Guibas, J-C. Latombe, S. M. LaValle, D. Lin, and R. Motwani. A visibility-based pursuit-evasion problem. International Journal of Computational Geometry and Applications, 9(4/5):471--, 1999.

No context found.

L. J. Guibas, J. Latombe, S. M. LaValle, D. Lin, and R. Motwani, "A visibility-based pursuit-evasion problem," International Journal of computational eometry and Applications, vol. 9, no. 5, pp. 471--494, October 1997.

No context found.

L.J. Guibas, J.C. Latombe, S.M. LaValle, D. Lin, and R. Motwani. A Visibility-Based Pursuit-Evasion Problem. International Journal of Computational Geometry and Applications, 9(5):471--494, 1999.

No context found.

L.J.Guibas,J.-C.Latombe,S.M.LaValle,D.Lin,and R. Motwani. A visibility-based pursuit-evasion problem. International Journal of Computational Geometry and Applications, 9(4/5):471--, 1999.

No context found.

L. J. Guibas, J.-C. Latombe, S. M. LaValle, D. Lin, and R. Motwani. A visibilitybased pursuit-evasion problem. International Journal of Computational Geometry and Applications, 9(4/5):471--, 1999.

No context found.

L. J. Guibas, J.-C. Latombe, S. M. LaValle, D. Lin, and R. Motwani. A visibility-based pursuit-evasion problem. International Journal of Computational Geometry and Applications, 9(4/5):471--, 1999.

No context found.

L. J. Guibas, J.-C. Latombe, S. M. LaValle, D. Lin, and R. Motwani. A visibilitybased pursuit-evasion problem. International Journal of Computational Geometry and Applications, 9(4/5):471--, 1999.

No context found.

L. J. Guibas, J.-C. Latombe, S. M. LaValle, D. Lin, and R. Motwani. A visibility-based pursuit-evasion problem. International Journal of Computational Geometry and Applications, 9(4/5):471--, 1999.

No context found.

L. J. Guibas, J.-C. Latombe, S. M. LaValle, D. Lin, and R. Motwani. A visibility-based pursuitevasion problem. International Journal of Computational Geometry and Applications (IJCGA), 9(4):471--493, 1999.

No context found.

L.J. Guibas, J.C. Latombe, S.M. Lavalle, D. Lin, and R. Motwani. A visibilitybased pursuit-evasion problem. Int. J. of Comp. Geom. and Appl., 9(4-5):471-493, 1999.

No context found.

L.J. Guibas, J.C. Latombe, S.M. Lavalle, D. Lin, and R. Motwani. A visibilitybased pursuit-evasion problem. Int. J. of Comp. Geom. and Appl., 9(4-5):471-493, 1999.

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