A. DATTA AND C. ICKING, Competitive searching in a generalized street, in Proc. 10th Annual ACM Symposium on Computational Geometry, Stony Brook, NY, June 6--8, 1994, ACM Press, New York, pp. 175--182.  Home/Search   Document Details and Download   Summary   Related Articles   Check

....Introduction Searching for a target is an important and well studied problem in robotics. In many realistic situations the robot does not possess complete knowledge about its environment, for instance, the robot may not have a map of its surroundings, or the location of the target may be unknown [3 6, 9, 11, 12, 14, 16, 17]. The search of the robot can be viewed as an on line problem since the robot s decisions about the search are based only on the part of its environment that it has seen so far. We use the framework of competitive analysis to measure the performance of an on line search strategy S [19] The ....

....This research is supported by the DFG Project Diskrete Probleme , No. Ot 64 8 1. The lower bound for searching in m rays has proved to be a very useful tool for proving lower bounds for searching in a number of classes of simple polygons, such as star shaped polygons [13] generalized streets [6, 15], HV streets [5] and streets [5, 8] In this paper we are interested in obtaining upper and lower bounds for the competitive ratio of parallel searching on m concurrent rays. This problem has been adressed before in two contexts. The rst context is the on line construction of hybrid ....

A. Datta and Ch. Icking. Competitive searching in a generalized street. In Proc. 10th Annu. ACM Sympos. Comput. Geom., pages 175-182, 1994.

....Introduction Searching for a target is an important and well studied problem in robotics. In many realistic situations the robot does not possess complete knowledge about its environment, for instance, the robot may not have a map of its surroundings, or the location of the target may be unknown [DI94, IK95, Kle92, LOS95, PY89]. Since the robot has to make decisions about the search based only on the part of its environment that it has explored before, the search of the robot can be viewed as an on line problem. One way to judge the performance of an on line search strategy is to compare the distance traveled by the ....

.... optimal competitive ratio is given by the minimum of the function 1 2a m = a 1) ln a) for a 1 [Gal80, KRT97, KMSY94] Searching on m rays has proven to be a very useful tool for searching in a number of classes of simple polygons, such as star shaped polygons [LOS97] generalized streets [DI94, LOS96], HV streets [DHS95] and streets [DHS95, Hip94] However, the proof of optimality for the above m way ray searching strategy relies on the unboundedness of the rays, that is, on the fact that the target can be placed arbitrarily far away from the starting point of the rays [BYCR93, Gal80] But, ....

[Article contains additional citation context not shown here]

A. Datta and Ch. Icking. Competitive searching in a generalized street. In Proc. 10th Annu. ACM Sympos. Comput. Geom., pages 175-182, 1994.

....arbitrary obstacles having a total of n vertices [2] even if we restrict ourselves to searching in a simple polygon. Therefore, the on line search problem has been studied previously for the case where the geometry of the terrain is restricted to searching in special classes of simple polygons [4, 5, 8, 16, 17]. In this paper we study the continuous angular bisector (CAB) strategy to search in street polygons. In a street P the starting point s and the target t are located on the boundary of P and This research is supported by the DFG Project Diskrete Probleme , No. Ot 64 8 2. y Faculty of ....

A. Datta and Ch. Icking. Competitive searching in a generalized street. In Proc. 10th ACM SoCG, pages 175-182, 1994.

....Introduction Searching for a target is an important and well studied problem in robotics. In many realistic situations the robot does not possess complete knowledge about its environment, for instance, the robot may not have a map of its surroundings, or the location of the target may be unknown [3 6, 9, 11, 12, 14, 16, 17]. The search of the robot can be viewed as an on line problem since the robot s decisions about the search are based only on the part of its environment that it has seen so far. We use the framework of competitive analysis to measure the performance of an on line search strategy S [19] The ....

....research is supported by the DFG Project Diskrete Probleme , No. Ot 64 8 1. 2 The lower bound for searching in m rays has proved to be a very useful tool for proving lower bounds for searching in a number of classes of simple polygons, such as star shaped polygons [13] generalized streets [6, 15], HV streets [5] and streets [5, 8] In this paper we are interested in obtaining upper and lower bounds for the competitive ratio of parallel searching on m concurrent rays. This problem has been adressed before in two contexts. The rst context is the on line construction of hybrid algorithms ....

A. Datta and Ch. Icking. Competitive searching in a generalized street. In Proc. 10th Annu. ACM Sympos. Comput. Geom., pages 175-182, 1994.

....Introduction Searching for a target is an important and well studied problem in robotics. In many realistic situations the robot does not possess complete knowledge about its environment, for instance, the robot may not have a map of its surroundings, or the location of the target may be unknown [DI94, IK95, Kle92, LOS95, PY89]. Since the robot has to make decisions about the search based only on the part of its environment that it has explored before, the search of the robot can be viewed as an on line problem. One way to judge the performance of an on line search strategy is to compare the distance traveled by the ....

.... competitive ratio is given by the minimum of the function 1 2a m = a Gamma 1) ln a) for a 1 [Gal80, KRT93, KMS94] Searching on m rays has proven to be a very useful tool for searching in a number of classes of simple polygons, such as star shaped polygons [LOS97] generalized streets [DI94, LOS96], HV streets [DHS95] and streets [DHS95, Hip94] However, the proof of optimality for the above m way ray searching strategy relies on the unboundedness of the rays, that is, on the fact that the target can be placed arbitrarily far away from the starting point of the rays [BYCR93, Gal80] But, ....

[Article contains additional citation context not shown here]

A. Datta and Ch. Icking. Competitive searching in a generalized street. In Proc. 10th Annu. ACM Sympos. Comput. Geom., pages 175--182, 1994.

....obstacles having a total of n vertices [4] even if we restrict ourselves to searching in a simple polygon. Therefore, the on line search problem has been studied previously in various contexts where the geometry of the obstacles is restricted such as searching in special classes of simple polygons [7, 8, 13, 22, 23], among rectangles [2, 3, 4, 5, 24, 25] convex polygons [14] and on the real line [1, 9, 10] This research is supported by the DFG Project Diskrete Probleme , No. Ot 64 8 2. y Faculty of Computer Science, University of New Brunswick, NB, E3B 5A3, Canada, e mail: alopez o unb.ca z ....

A. Datta and Ch. Icking. Competitive searching in a generalized street. In Proc. 10th ACM Symp. on Computational Geometry, pages 175--182, 1994.

....Introduction Searching for a target is an important and well studied problem in robotics. In many realistic situations the robot does not possess complete knowledge about its environment, for instance, the robot may not have a map of its surroundings, or the location of the target may be unknown [DI94, IK95, Kle92, LOS95, PY89]. Since the robot has to make decisions about the search based only on the part of its environment that it has explored before, the search of the robot can be viewed as an on line problem. One way to judge the performance of an on line search strategy is to compare the distance traveled by the ....

....Institut fur Informatik, Am Flughafen 17, Geb. 051, D 79110 Freiburg, Germany email: schuiere informatik.uni freiburg.de 1 Searching on m rays has proven to be a very useful tool for searching in a number of classes of simple polygons, such as star shaped polygons [LOS97] generalized streets [DI94, LOS96], HV streets [DHS95] and streets [DHS95, Hip94] Hipke et al. consider the maximal reach of a strategy to search on the line if the competitive ratio of the strategy is given [HIKL97] The reach of a strategy X with competitive ratio C is the maximum distance D such that a target placed at a ....

A. Datta and Ch. Icking. Competitive searching in a generalized street. In Proc. 10th Annu. ACM Sympos. Comput. Geom., pages 175--182, 1994.

....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 ....

....ratios can be achieved. Klein [6] introduced a class of polygons called streets. He gave a 1 3 2 ( 5:72) competitive strategy for finding the target in a street and also proves a lower bound of p 2. Kleinberg [9, 8] improved this ratio to 1 p 4 p 8 ( 2 p 2) Datta and Icking [2] generalized the class of streets, called G streets. They showed a lower bound of 9 and present a 9 competitive (9:06 competitive) strategy for rectilinear G streets under the L 1 (L 2 ) norm. As another class of polygons, we consider the class of star shaped polygons. A polygon P is star shaped ....

[Article contains additional citation context not shown here]

A. Datta and Ch. Icking. Competitive searching in a generalized street. In Proc. 10th Annu. ACM Sympos. Comput. Geom., pages 175--182, 1994.

....also present a different strategy which is a modification of Dijkstra s shortest path algorithm with a competitive ratio of 2n Gamma 7. Our algorithms work in any simple polygon. This should be contrasted with previous search algorithms that require restricted classes of polygons as their input [DHS95, DI94, Kle92, Kle94, LOS96, LOS97]. The paper is organized as follows. In the next section we introduce some definitions. In Section 3 we present the algorithm to search in a geometric tree and analyse its competitive ratio. Section 4 shows how the algorithm can be applied to searching in a simple polygon. It also introduces a ....

A. Datta and Ch. Icking. Competitive searching in a generalized street. In Proc. 10th Annu. ACM Sympos. Comput. Geom., pages 175--182, 1994.

....1 Introduction Searching for a goal is an important and well studied problem in robotics. In many realistic situations the robot does not possess complete knowledge about its environment, for instance, the robot may not have a map of its surroundings or the location of the goal may be unknown [BRS93, CL93, DHS95, DI94, IK95, Kle92, Kle94, LOS95, MI94, PY89]. Since the robot has to make decisions about the search based only on the part of its environment that it has explored before, the search of the robot can be viewed as an on line problem. This invites the application of competitive analysis to judge the performance of an on line search strategy. ....

....contains the This research is supported by the DFG Project Diskrete Probleme , No. Ot 64 8 2. goal g whose distance to the origin is unknown. The robot can only detect g if it stands on top of it. Many problems of searching in more complex geometries can be reduced to searching on m rays [DI94, LOS97, LOS96, DHS95]. In the deterministic case Baeza Yates et al. BYCR93] and Gal [Gal80] present an optimal search strategy that achieves a competitive ratio of 1 2m m = m Gamma 1) m Gamma1 . In the randomized case Kao, Reif, and Tate [KRT93] present an optimal randomized algorithm to search on m rays and ....

A. Datta and Ch. Icking. Competitive searching in a generalized street. In Proc. 10th Annu. ACM Sympos. Comput. Geom., pages 175--182, 1994.

....Introduction Searching for a target is an important and well studied problem in robotics. In many realistic situations the robot does not possess complete knowledge about its environment, for instance, the robot may not have a map of its surroundings, or the location of the target may be unknown [BRS93, CL93, DHS95, DI94, IK95, Kle92, Kle94, LOS95, MI94, PY89]. The search of the robot can be viewed as an on line problem since the robot s decisions about the search are based only on the part of its environment that it has seen so far. We use the framework of competitive analysis to measure the performance of an on line search strategy S [ST85] The ....

.... Cm achieved by this strategy is given by 1 2 m m (m Gamma 1) m Gamma1 : The lower bound for searching in m rays has proved to be a very useful tool for proving lower bounds for searching in a number of classes of simple polygons, such as star shaped polygons [LO96] generalized streets [DI94, LOS96], HV streets [DHS95] and streets [DHS95, Hip94] In this paper we are interested in obtaining upper and lower bounds for the competitive ratio of parallel searching on m concurrent rays. This problem has been adressed before in two contexts. The first context is the on line construction of ....

A. Datta and Ch. Icking. Competitive searching in a generalized street. In Proc. 10th Annu. ACM Sympos. Comput. Geom., pages 175--182, 1994.

....and Schuierer [12] presented an online strategy, which has a better competitive ratio of 2 p 1 (1 4 ) 2 ( 2:05) Recently, they presented a hybrid strategy [11] which achieves a competitive ratio of 1:73 improving significantly the previous best known result. Datta and Icking [3] defined a new, strictly larger class of simple polygons, so called Generalized streets (G streets, for short) and presented an on line strategy which achieves an optimal 9 competitive ratio (resp. p 82 competitive) in Manhattan metric L 1 ( resp. L 2 ) metric to search in an unknown ....

R. A. Baeza - Y A. Datta and C. Icking. Competitive searching in a generalized street. In 10th ACM Computational Geometry, pp. 175182, 1994.

....the competitive ratio of the strategy. Since there is no strategy with a competitive ratio of o(n) for scenes with arbitrary obstacles having a total of n vertices [2] the on line search problem has been studied previously in various contexts where the geometry of the obstacles is restricted [1, 2, 3, 4, 10, 11]. Klein introduced the notion of a street which allowed for the first time a search strategy with a constant competitive ratio [7] In a street, the starting points s and the goal g are located on the boundary of the polygon and the two polygonal chains from s to g are mutually weakly visible. ....

A. Datta and Ch. Icking. "Competitive searching in a generalized street", Proc. of 10th ACM Sypm. on Computational Geometry, (1994), pp. 175-182.

....travel more than p 2 times the diagonal. Curiously enough, this is the only known lower bound even for arbitrarily oriented streets. Finally, a more general class of polygons, called G streets, has been introduced by Datta and Icking that allows search strategies with a competitive ratio of 9:06 [5]. In this paper we present several strategies to traverse a street. All of them are similar to the original approach presented by Klein. The first strategy which can been viewed as a class of strategies, is called Walk in Circles and presents a very simple criterion for the robot to advance. Its ....

A. Datta and Ch. Icking. "Competitive searching in a generalized street", Proc. 10th ACM Symp. on Computational Geometry, (1994), pp. 175-182.

....more than p 2 times the diagonal. Curiously enough, this is the only known lower bound even for arbitrarily oriented streets. Finally, a more general class of polygons, called G streets, has been introduced by Datta and Icking that allows search strategies with a competitive ratio of 9:06 [4]. All the these strategies fall into the category of Unknown Destination Searches (UDS) in which the location of the goal is unknown. One natural source of information for the robot are the coordinates of the target. The first problem we consider is a lower bound for strategies for Known ....

.... Gamma O(1= p n) competitive ratio, which in the limit is p 2. As it can be seen, regardless of the policy, a p 2 inefficiency factor is necessarily introduced, even in the case where the robot knows where it is going, but is ignorant of the terrain in which is moving. 2 Datta and Icking [4] introduced the notion of G streets and showed for the UDS problem a competitive ratio of 9.06. Definition 3.3 ( 4] A simple polygon in the plane is called a generalized street if for every boundary point p 2 L [ R, there exists a horizontal chord with end points in L and R and from which p ....

[Article contains additional citation context not shown here]

A. Datta and Ch. Icking. "Competitive searching in a generalized street", Proc. of 10th ACM Sypm. on Computational Geometry, (1994), pp. 175-182.

No context found.

A. Datta and C. Icking. Competitive searching in a generalized street. In Proc. 10th Annu. ACM Sympos. Comput. Geom., pages 175--182, 1994.

....of less than # 2 1.41, the ultimative lower bound to the ratio as turned out later. Since then, street polygons have attracted considerable attention concerning structural properties, generalizations and applications in related fields, see Tseng et al. 43] Das et al. 9] Datta and Icking [12,13], Datta et al. 11] LopezOrtiz and Schuierer [32,35] Ghosh and Saluja [17] Brocker and Schuierer [7] Carlsson and Nilsson [8] Brocker and Lopez Ortiz [6] have shown that a constant performance ratio can be achieved for arbitrary start and endpoints inside a street. The main research has ....

A. Datta and C. Icking. Competitive searching in a generalized street. Comput. Geom. Theory Appl., 13:109--120, 1999.

....of less than # 2 1.41, the ultimative lower bound to the ratio as turned out later. Since then, street polygons have attracted considerable attention concerning structural properties, generalizations and applications in related fields, see Tseng et al. 43] Das et al. 9] Datta and Icking [12,13], Datta et al. 11] LopezOrtiz and Schuierer [32,35] Ghosh and Saluja [17] Brocker and Schuierer [7] Carlsson and Nilsson [8] Brocker and Lopez Ortiz [6] have shown that a constant performance ratio can be achieved for arbitrary start and endpoints inside a street. The main research has ....

A. Datta and C. Icking. Competitive searching in a generalized street. In Proc. 10th Annu. ACM Sympos. Comput. Geom., pages 175--182, 1994.

....properties. Tseng et al. 24] have shown how to report all pairs of vertices (s, t) of a given polygon for which it is a street; for star shaped polygons many of such vertex pairs exist. Das et al. 6] have improved on this result by giving an optimal linear time algorithm. Datta and Icking [9] introduced generalized streets, a concept further generalized by Datta et al. 8] and by Lopez Ortiz and Schuierer [18] Ghosh and Saluja [10] have described how to walk an unknown street incurring a minimum number of turns. Other research addressed the gap between the # 2 lower bound and the ....

A. Datta and C. Icking. Competitive searching in a generalized street. In Proc. 10th Annu. ACM Sympos. Comput. Geom., pages 175--182, 1994.

....# 2 # 1.414. Finally, in Section 4 we show that # 2remainsa lower bound for searching in orthogonal streets even if the location of the goal is knowninadvance. Competitive on line searching has also been investigated in many other settings such as searching in other classes of simple polygons [6, 7, 11, 18, 20], among rectangles [2, 3, 4, 5, 21, 22] convex polygons [12] and on the real line [1, 8, 9] 2 Searching for a goal in a street In our model the room is a simple polygon P in the plane, the robot is just a point moving inside the polygon, and the start position s and the goal t are two of P s ....

A. Datta and C. Icking. Competitive searching in a generalized street. In Proc. 10th Annu. ACM Sympos. Comput. Geom., pages 175--182, 1994.

.... 2.24. We have the interesting situation that these strategies are theoretically better than lad with its 4.44 performance, but in practise, lad turns out to be superior. For the rectilinear case, a class of polygons called G streets, which includes streets, has been found by Datta and Icking [4], which can be searched with a competitive factor of 9. Datta et al. 3] give further generalizations of this. A di#erent approach has been considered by Ghosh and Saluja [8] they count the number of turns and not the length of a path. 3 Learning an unknown environment In contrast to the ....

A. Datta and C. Icking. Competitive searching in a generalized street. In Proc. 10th Annu. ACM Sympos. Comput. Geom., pages 175--182, 1994.

....the number of turns. Many results on competitive search algorithms have appeared. For example, Blum et al. 4] have studied several problems involving obstacles. Special polygons called streets have been investigated by Klein [18] Kleinberg [19] Lopez Ortiz and Schuierer [20] Datta and Icking [8], and Ghosh and Saluja [12] Relatively few competitive strategies are known for learning an unknown environment. Icking, Klein, and Ma [17] gave an optimal competitive strategy for looking around a single corner. Recently Icking and Klein [16] have shown how to find the closest point in an ....

A. Datta and C. Icking. Competitive searching in a generalized street. In Proc. 10th Annu. ACM Sympos. Comput. Geom., pages 175--182, 1994.

No context found.

A. DATTA AND C. ICKING, Competitive searching in a generalized street, in Proc. 10th Annual ACM Symposium on Computational Geometry, Stony Brook, NY, June 6--8, 1994, ACM Press, New York, pp. 175--182.

No context found.

Amitava Datta and Christian Icking. Competitive Searching in a Generalized Street. In Proceedings of the Tenth Annual Symposium on Computational Geometry, pages 175--182, Stony Brook, NY, June 6--8 1994. ACM Press.

No context found.

A. Datta and Ch. Icking. \Competitive searching in a generalized street", Proceedings 10th ACM Symposium on Computational Geometry, (1994), pp. 175182.

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