F. Homann, C. Icking, R. Klein, and K. Kriegel. A competitive strategy for learning a polygon. In Proceedings of the 8th ACM-SIAM Symposium on Discrete Algorithms (SODA'97), pages 166-174, 1997.  Home/Search   Document Not in Database   Summary   Related Articles   Check

.... Previous Work Exploration and navigation in unknown terrains is a well studied problem, see the survey of Rao et al. [17] The exploration can be modeled geometrically as shown by Blum, Raghavan, and Schieber [10] Bar Eli, Berman, Fiat, and Yan [5] Deng and Papadimitriou [12] and Ho mann et al. [14]. Papadimitriou and Yanakakis [16] consider nding shortest paths in various unknown graphs and Blum and Chalasani [9] give a k trip shortest path algorithm. The exploration can also be modeled with a nite state automata as shown by Rivest and Schapire [18] or as a graph. In the later case the ....

F. Homann, C. Icking, R. Klein, and K. Kriegel. A competitive strategy for learning a polygon. In Proceedings of the 8th Annual Symposium on Discrete Algorithms (SODA), pages 166-174, 1997.

.... Previous Work Exploration and navigation in unknown terrains is a well studied problem (see the survey of Rao et al. [17] The exploration can be modeled geometrically as shown by Blum, Raghavan, and Schieber [10] Bar Eli, Berman, Fiat, and Yan [5] Deng and Papadimitriou [12] and Ho mann et al. [14]. Papadimitriou and Yanakakis [16] consider nding shortest paths in various unknown graphs and Blum and Chalasani [9] give a k trip shortest path algorithm. The exploration can also be modeled with a nite state automata as shown by Rivest and Schapire [18] or as a graph. In the later case the ....

F. Homann, C. Icking, R. Klein, and K. Kriegel. A competitive strategy for learning a polygon. In Proceedings of the 8th Annual Symposium on Discrete Algorithms (SODA), pages 166-174, 1997.

....26, 36, 25] We note that Dean et al. 17] apply a cycling technique related to ours, but for di erent purposes. For a survey covering some of the results mentioned above among others, see [18] Exploring and navigating in geometric environments is studied extensively. A sample of papers includes [7, 31, 19, 14, 8, 13, 11, 27, 4]. Applications. As mentioned earlier, algorithms for exploring and mapping unknown environments have a variety of applications. Examples are obtaining maps of existing networks (e.g. computer networks, sewage systems, unexplored caves) for which there are no maps or the existing maps are ....

F. Homan, C. Icking, R. Klein, and K. Kriegel. A competitive strategy for learning a polygon. In Proceedings of the Eighth Annual ACM-SIAM Symposium on Discrete Algorithms, pages 166-174, 1997.

....path in the polygon. The competitive ratio is the worst case ratio achieved over all possible problem instances. A strategy is called competitive if its competitive ratio is constant. In recent years, the competitive searching in unknown polygons has been intensively studied by many researchers [1, 3, 6, 2, 9, 5, 4] in computational geometry. Since it is impossible to competitively find a target in general polygons [6, 9] most of the work has focused on restricting the classes of polygons for which constant competitive ratios can be achieved. Klein [6] introduced a class of polygons called streets. He gave ....

F. Hoffmann, C. Icking, R. Klein, and Klaus Kriegel. A competitive strategy for learning a polygon. In Proc. 8th SODA, page to be appeared, 1997.

....robots can learn a directed graph with indistinguishable nodes, where each node has the same number of outgoing edges. Subsequent to the work in [12] Deng et al. 11] investigated a geometric exploration problem, whose goal is to explore a room with or without polygonal obstacles. Hoffmann et al. [15] gave an improved exploration strategy for rooms without obstacles. More generally, theoretical studies of exploration and navigation problems in unknown environments were initiated by Papadimitriou and Yannakakis [18] They considered the problem of finding a shortest path from a point s to a ....

F. Hoffmann, C. Icking, R. Klein and K. Kriegel. A competitive strategy for learning a polygon. Proc. 8th ACM-SIAM Symp. on Discrete Algorithms, 166--174, 1997.

....robots can learn a directed graph with indistinguishable nodes, where each node has the same number of outgoing edges. Subsequent to the work in [9] Deng et al. 8] investigated a geometric exploration problem, whose goal is to explore a room with or without polygonal obstacles. Hoffmann et al. [11] gave an improved exploration strategy for rooms without obstacles. More generally, theoretical studies of exploration and navigation problems in unknown environments were initiated by Papadimitriou and Yannakakis [13] They considered the problem of finding a shortest path from a point s to a ....

F. Hoffmann, C. Icking, R. Klein and K. Kriegel. A competitive strategy for learning a polygon. Proc. 8th ACM-SIAM Symp. on Discrete Algorithms, 166--174, 1997.

....robots can learn a directed graph with indistinguishable nodes, where each node has the same number of outgoing edges. Subsequent to the work in [12] Deng et al. 11] investigated a geometric exploration problem, whose goal is to explore a room with or without polygonal obstacles. Hoffmann et al. [15] gave an improved exploration strategy for rooms without obstacles. More generally, theoretical studies of exploration and navigation problems in unknown environments were initiated by Papadimitriou and Yannakakis [18] They considered the problem of finding a shortest path from a point s to a ....

F. Hoffmann, C. Icking, R. Klein and K. Kriegel, A competitive strategy for learning a polygon, in Proc. 8th ACM-SIAM Symp. on Discrete Algorithms, 1997, pp. 166--174.

....problem that do not rely on a teacher are studied in the following works [14, 18, 28, 17] We note that Dean et al. 14] apply a cycling technique related to ours, but for different purposes. Exploring and navigating in geometric environments is studied extensively. A sample of papers includes [5, 23, 15, 11, 6, 10, 8, 19, 2]. 2 Preliminaries Let G = V;E) be the unknown directed graph the robot has to explore and map. Suppose that the graph is strongly connected and that all the vertices of G are unlabeled and have (the same) outdegree d. Let the edges emanating from each vertex be labeled by distinct indices in ....

F. Hoffman, C. Icking, R. Klein, and K. Kriegel. A competitive strategy for learning a polygon. In Proceedings of the Eighth Annual ACM-SIAM Symposium on Discrete Algorithms, pages 166--174, 1997.

....of this problem that do not rely on a teacher are studied in the following works [14, 18, 27, 17] We note that Dean et al. 14] apply a cycling technique related to ours for different purposes. Exploring and navigating in geometric environments is studied extensively. A sample of papers includes [5, 22, 15, 11, 6, 10, 8, 19, 2]. 2 Preliminaries Let G = V; E) be the unknown directed graph the robot explores and maps. Suppose that the graph is strongly connected and that all the vertices of G are unlabeled and have (the same) outdegree d. Let the edges emanating from each vertex be labeled by distinct indices in f1; ....

F. Hoffman, C. Icking, R. Klein, and K. Kriegel. A competitive strategy for learning a polygon. In Proceedings of the Eighth Annual ACM-SIAM Symposium on Discrete Algorithms, pages 166--174, 1997.

.... the exploration of unknown environments, and the problem was further investigated by Betke [8] and Blum et al. 10] The geometric aspect of the navigation problem (in the context of room exploration with or without polygonal obstacles) has been examined by Deng et al. 12] and Hoffmann et al. [14]. On line naviagaiton was studied by Blum et al. 10] and Bar Eli et al. 4] Recently, randomized robot navigation was addressed by Berman et al. 6] while Bender and Slonim [5] examined graph exploration by two robots. A survey of robot navigation problems and algorithms can be found in Rao et ....

F. Hoffmann, C. Icking, R. Klein and K. Kriegel. A competitive strategy for learning a polygon. In 8th Symposium on Discrete Algorithms, pages 166-174, January 1997.

....deterministic algorithm [135, 136] and a 5 4 competitive randomized algorithm [242] for the exploration problem. For general simple polygons, the competitive ratio of [135] is proved to be constant, but is only estimated to be in the thousands. A bound of 133 was later given by Hoffman et al. [211], and has recently been improved to (18 p 2 1) 26:5 by the same set of authors [212] Kalyanasundaram and Pruhs [231] study the search and explore problems for a vision equipped robot among a set of k disjoint convex obstacles having average aspect ratio 5 ff. They obtain tight bounds on ....

F. Hoffmann, C. Icking, R. Klein, and K. Kriegel. A competitive strategy for learning a polygon. In Proc. 8th ACM-SIAM Sympos. Discrete Algorithms, pages 166--174, 1997.

....a complete map of that environment using a short path. Localization: The robot has a map of the environment. It wakes up at a position s and has to uniquely determine its initial position using a short path. In the following we concentrate on the robot navigation problem. We refer the reader to [4, 35, 36, 44] for literature on the exploration problem, and to [37, 43, 51, 63] for literature on the localization problem. Many robot navigation problems were introduced by Baeza Yates et al. 13] and Papadimitriou and Yannakakis [59] We call an robot navigation A strategy c competitive, if the length of ....

F. Hoffmann, C. Icking, R. Klein and K. Kriegel. A competitive strategy for learning a polygon. Proc. 8th ACM-SIAM Symp. on Discrete Algorithms, 166--174, 1997.

No context found.

F. Ho#mann, C. Icking, R. Klein, and K. Kriegel. A competitive strategy for learning a polygon. In Proc. 8th Annual ACM-SIAM Symposium on Discrete Algorithms, 1997.

....competitive factor of 2016. For the rectilinear case, they gave a complete, and elegant, proof in [9] here a simple greedy strategy can be applied that performs surprisingly well. The first proof for the more di#cult case of non rectilinear simple polygons has been given in our conference paper [11]. There we have provided an on line exploration strategy and sketched a proof that the tour it generates in any polygon is shorter than 133 times the length of the optimum watchman tour. One of the main di#culties with this analysis was in establishing reasonably sharp length estimates for robot ....

....tour. In the absence of holes, the robot has seen each point inside the polygon as soon as it has seen each point on its boundary. The present paper contains the first complete presentation and analysis of an exploration strategy for simple polygons. As compared to the conference version [11], this full paper has been greatly simplified, and describes a new analysis that is built on an interesting geometric relation between the robot s path and the optimum watchman tour. This relation is expressed in terms of the angle hull,anovelgeometric structure introduced in Part II of this ....

F. Ho#mann, C. Icking, R. Klein, and K. Kriegel. A competitive strategy for learning a polygon. In Proc. 8th ACM-SIAM Sympos. Discrete Algorithms, pages 166--174, 1997.

....implemented as an online strategy. For the rectilinear case, they gave a complete and elegant proof in [12] here the greedy strategy can be applied that performs surprisingly well. The first proof for the more di#cult case of non rectilinear simple polygons has been given in our conference paper [15]. There we have provided an on line exploration strategy and sketched a proof that the tour it generates in any polygon is not longer than 133 times the length of the optimum watchman tour. One of the main di#culties with this analysis was in establishing reasonably sharp length estimates for ....

....in establishing reasonably sharp length estimates for robot paths of complex structure, and in relating them to the optimum watchman tour. The present paper contains the first complete presentation and analysis of an exploration strategy for simple polygons. As compared to the conference version [15], this full paper has been greatly simplified and describes a new analysis that is built on an interesting geometric relation between the robot s path and the optimum watchman tour. This relation is expressed in terms of the angle hull, a novel geometric structure. With these improvements we are ....

F. Hoffmann, C. Icking, R. Klein, and K. Kriegel, A competitive strategy for learning a polygon, in Proc. 8th ACM-SIAM Sympos. Discrete Algorithms, 1997, pp. 166--174.

.... by an optimal # 2 competitive strategy by Icking et al. 16] and, independently, by Schuierer et al. 33] Other interesting geometric applications for competitive strategies are e.g. the search for the kernel of a polygon [15,24,28,22] exploration or path planning in unknown environments [7,11,12,1,6], or localization in known environments [8,10,14,19,32] It has been posed as a challenging open problem whether more general classes 2 of polygons admit competitive searching. In this paper, we introduce such a class of polygons, namely the generalized streets,orG streets for short. We give a ....

F. Ho#mann, C. Icking, R. Klein, and K. Kriegel. A competitive strategy for learning a polygon. In Proc. 8th ACM-SIAM Sympos. Discrete Algorithms, pages 166--174, 1997.

No context found.

F. Homann, C. Icking, R. Klein, and K. Kriegel. A competitive strategy for learning a polygon. In Proceedings of the 8th ACM-SIAM Symposium on Discrete Algorithms (SODA'97), pages 166-174, 1997.

No context found.

F. Hoffman, C. Icking, R. Klein, and K. Kriegel. A competitive strategy for learning a polygon. In Proceedings of the Eighth Annual ACM-SIAM Symposium on Discrete Algorithms, pages 166--174, 1997.

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