A. Blum, P. Raghavan, and B. Schieber. Navigating in unfamiliar geometric terrain. In Proc. 23rd ACM STOC, 1991.  Home/Search   Document Details and Download   Summary   Related Articles   Check

....Exploration and navigation problems for robots in an unknown environment have been extensively studied in the literature (cf. the survey [26] There are two groups of models for these problems. In one of them a particular geometric setting is assumed, e.g. unknown terrain with convex obstacles [10], or room with polygonal [14] or rectangular [5] obstacles. Another approach is to model the environment as a graph, assuming that the robot may only move along its edges. The graph setting can be further speci ed in two di erent ways. In [1, 7, 8, 15] the robot explores strongly connected ....

A. Blum, P. Raghavan and B. Schieber, Navigating in unfamiliar geometric terrain, SIAM Journal on Computing 26 (1997), 110-137.

....exceed c times the cost of solving P in an optimal way, given full information. The minimum c satisfying this condition is called the competitive factor of S. Among other work, competitive geometric algorithms have been developed by Papadimitriou and Yanakakis [10] Blum, Raghhavan, and Schieber [2], and Eades, Lin, and Wormald [5] for path planning in the presence of obstacles in the plane, by Deng, Kameda, and Papadimitriou [4] for learning the interior of a polygon that may have a bounded number of holes, and by Klein [7] for finding a path in the interior of special simple polygons ....

A. Blum, P. Raghavan, and B. Schieber. Navigating in unfamiliar geometric terrain. In Proceedings of the 23rd ACM Symposium on Theory of Computing, 1991, pp. 494--504.

....is when all obstacles are axisparallel rectangles of width at least 1 located in the in nite Euclidean plane. Natural greedy strategies yield a competitive ratio of (n) where n is the Euclidean source target distance. More sophisticated algorithms obtain competitive ratios of ( p n) BRS91] Randomized algorithms can do much better [BBF 96] Through the use of randomization, one can translate the case of arbitrary convex obstacles [BRS91] to rectilinearly aligned rectangles, at the cost of some increase in the competitive ratio. If the scene is not on an in nite plane but ....

....ratio of (n) where n is the Euclidean source target distance. More sophisticated algorithms obtain competitive ratios of ( p n) BRS91] Randomized algorithms can do much better [BBF 96] Through the use of randomization, one can translate the case of arbitrary convex obstacles [BRS91] to rectilinearly aligned rectangles, at the cost of some increase in the competitive ratio. If the scene is not on an in nite plane but rather within some nite rectangular warehouse, and the start location is one of the warehouse corners, then the competitive ratio drops to log n [BBFY92] ....

A. Blum, P. Raghavan, and B. Schieber. Navigating in unfamiliar geometric terrain. In Proc. 23rd Annu. ACM Sympos. Theory Comput., pages 494-504, 1991.

....simple polygon by doubling on the shortest path tree, with an optimal competitive ratio proportional to the number of vertices. A similar approach has recently enabled Lopez Ortiz and Schuierer [7] to find a target point in a star shaped polygon with a constant competitive ratio. Blum et al. [2] and Kalyanasundaram and Pruhs [4] are both drawing on the basic idea behind the doubling technique: After an unsuccessful attempt, one can a#ord doubling the e#ort as long as it does not exceed a constant times the cost of the optimal solution. In their paper [1] Baeza Yates et al. have also ....

A. Blum, P. Raghavan, and B. Schieber. Navigating in unfamiliar geometric terrain. SIAM J. Comput., 26(1):110--137, Feb. 1997.

....cost A (#) c cost OPT (#) b The competitive ratio is the infimum over c such that A is c competitive. We say that an algorithm is competitive, if it has a constant competitive ratio. In robotics, competitive analysis has been used for various navigation problems as a measure of efficiency [4], 9] 1] 12] 8] 11] In the context of exploration, the competitive ratio gives us the worst case deviation of the cost of an exploration algorithm from the cost incurred by a robot who has a prior model of the environment and still wants to build a map. B. Competitive analysis in robot ....

A. Blum, P. Raghavan, and B. Schieber. Navigating in unfamiliar geometric terrain. SIAM Journal on Computing, 26(1):110--137, 1997.

....until you succeed and the relative ease of analyzing the performance guarantee one gets the sum of all that you ve done in previous phases is only a constant fraction of what you do in the current phase. Recently, it has been used in many of the robot search papers we will discuss below [BCR, PY, BRaSc, KRT, Kl], an abstract kind of navigation problem known as layered graph traversal [PY, FFKRRV] the design of hybrid algorithms [KMSY] and even the approximation of some NP hard problems [BCCPRS, TWSY] s t Figure 2 1: A rectangle packing The work of Papadimitriou and Yannakakis followed [BCR] and ....

....ratio 26 1:70, and shows that no on line algorithm can be better than 2 competitive. For the case of an arbitrary rectangle packing, no bounded competitive ratio is possible: PY] shows a lower bound of Omega Gamma n) on the best possible competitive ratio. Blum, Raghavan, and Schieber [BRaSc] address the same type of shortest paths problems and give an O( n) competitive algorithm for the s t path problem in a rectangle packing; this matches the lower bound of [PY] up to constant factors. BRaSc] also introduced the elegant room problem consider a rectangle packing inside a ....

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A. Blum, P. Raghavan, B. Schieber, "Navigating in unfamiliar geometric terrain," Proc. 23rd ACM Symposium on Theory of Computing, 1991, pp. 494--504.

....of machine learning. It is about the design and analysis of efficient learning algorithms for confident explorers. Similar formal approaches to environment learning have been studied previously in the context of graph theory, computational geometry, on line algorithms, and automata theory (e.g. [89, 21, 93]) In this related work, formal models are defined that try to capture the difficulties that lie in the confident explorer s limited knowledge of its environment. In our work, we assume that the unknown environment can be described by a simple discrete model, an undirected graph G = V; E) We ....

....If the obstacles are arbitrarily sized, axis aligned squares, their algorithm has a competitive ratio of 1=2 26 1:7. They also provide a lower bound of Omega Gamma n) for this problem where n is the shortest distance between s and t. This bound is matched by Blum, Raghavan, and Schieber [21]. They describe an O( competitive algorithm for the case that the goal is on an infinite wall. They also give an O(n2 log n ) algorithm for the case that the environment can be modeled as 20 a two dimensional room where s is on the wall of the room and t in the center. This result is ....

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Avrim Blum, Prabhakar Raghavan, and Baruch Schieber. Navigating in unfamiliar geometric terrain. In Proceedings of Twenty-Third ACM Symposium on Theory of Computing, pages 494--504. ACM, 1991. 121

....ratio is Omega Gamma n) where n is the length of the shortest path between the start and goal locations. For the case of square obstacles, they give a 26 1:7 competitive algorithm, and show that any strategy must have competitive ratio greater than 2 . Blum, Raghavan, and Schieber [22] also study the problem of point to point navigation in 3.3 Formal model 39 an unknown two dimensional geometric environment with convex obstacles. For the case of axis parallel rectangular obstacles, they give an algorithm with competitive ratio O( n) matching the lower bound of Papadimitriou ....

....sides have the same number of edges. A 1 Theta 1 face might correspond to a standard city block; larger faces might correspond to obstacles (parks or shopping malls) Figure 3.3 gives an example. City block graphs are also studied by Papadimitriou and Yanakakis [62] Blum, Raghavan, and Schieber [22], and Bar Eli, Berman, Fiat and Yan [10] An m Theta n city block graph with no obstacles has exactly mn vertices (at points (i; j) for 1 i m, 1 j n) and 2mn Gamma (m n) edges (between points at distance 1 from each other) Obstacles, if present, decrease the number of accessible ....

Avrim Blum, Prabhakar Raghavan, and Baruch Schieber. Navigating in unfamiliar geometric terrain. In Proceedings of Twenty-Third ACM Symposium on Theory of Computing, pages 494--504. ACM, 1991.

....algorithm, optimum watchman tour, polygon, robot. 1 Introduction In the last decade, the path planning problem of autonomous mobile systems has received a lot of attention in the communities of robotics, computational geometry, and on line algorithms; see e.g. Rao et al. 17] Blum et al. [4], and the upcoming surveys by Mitchell [15] in Sack and Urrutia [18] and by Berman [3] in Fiat and Woeginger [10] We are interested in strategies that are correct, in that the robot will accomplish its mission whenever this is possible, and in performance guarantees that allow us to relate the ....

A. Blum, P. Raghavan, and B. Schieber. Navigating in unfamiliar geometric terrain. SIAM J. Comput., 26(1):110--137, Feb. 1997. 20

....noise remains an open problem. The question is further complicated by the fact that the choice of an optimal mapping strategy is sensitive to the specific task at hand. A somewhat distinct research stream deals with the complexity issues in autonomous robot exploration of an unknown environment [5, 16, 21, 17]. In general, work on sensor fusion has tended to focus on issues of how best to combine measurements from di#erent sensors e.g. 24, 6] or how best to extract data with a single sensor and fuse the measurements over time e.g. 11, 12, 25] rather than how to selectively extract measurements from ....

Avrim Blum, Prabhakar Raghavan, and Baruch Schieber. Navigating in unfamiliar geometric terrain. In Proc. 23rd ACM Symposium on the Theory of Computing, pages 494--504. ACM Press, 1991.

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A. Blum, P. Raghavan, and B. Schieber. Navigating in unfamiliar geometric terrain. In Proc. 23rd ACM STOC, 1991.

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A. Blum, P. Raghavan, and B. Schieber. Navigating in Unfamiliar Geometric Terrain. In Proc. 23rd ACM STOC, 1991.

....you have even more information and so on. What is a strategy that allows your path taken each time to be good, and to improve with experience Perhaps you might even design your paths explicitly so as to gain more information for future trips. Specifically, we consider the scenario (examined in [17, 7, 11, 10]) where there is a start point and target in a 2 dimensional plane filled with non overlapping, axis parallel rectangular obstacles, This material is based upon work supported under NSF National Young Investigator grant CCR 9357793 and a Sloan Foundation Research Fellowship. having ....

....positions and extents of the obstacles; it only finds out of their existence as it bumps into them. In the problem considered in previous papers, the robot s goal is to travel from as quickly as possible. We call this the one trip problem. For this problem, is the Euclidean distance, [7] presents an algorithm that guarantees an the distance traveled to the shortest path length, which is known to be optimal for deterministic algorithms [17] Here, we consider the situation where the robot may be asked to make multiple . We would like an intelligent strategy for the ....

[Article contains additional citation context not shown here]

A. Blum, P. Raghavan, and B. Schieber. Navigating in unfamiliar geometric terrain. In Proc. 23rd ACM STOC, 1991.

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Blum, A., Raghavan, P., and Schieber, B. (1991), Navigating in unfamiliar geometric terrain, in "Proceedings, 23rd ACM Symposium on Theory of Computing," pp. 494--504.

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A. BLUM,P .RAGHAVAN AND B. SCHIEBER, Navigating in unfamiliar geometric terrain,in Proc. 23rd Annual ACM Symposium on Theory of Computing, ACM, New York,

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Avrim Blum, Prabhakar Raghavan, and Baruch Schieber. Navigating in unfamiliar geometric terrain. SIAM Journal on Computing, 26:110--137, 1997.

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Avrim Blum, Prabhakar Raghavan, and Baruch Schieber. Navigating in unfamiliar geometric terrain. SIAM Journal on Computing, 26:110--137, 1997.

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A. Blum, P. Raghavan and B. Schieber, Navigating in unfamiliar geometric terrain, SIAM Journal on Computing, 26, (1997), 110-137.

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A. Blum, P. Raghavan, and B. Schieber. Navigating in unfamiliar geometric terrains. In Proc. ACM Symposium on Computational Geometry, pages 494-- 504, 1991.

No context found.

A. Blum, P. Raghavan, and B. Schieber. Navigating in unfamiliar geometric terrain. SIAM Journal on Computing, 26(1):110--137, 1997.

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Avrim Blum, Prabhakar Raghavan, and Baruch Schieber. Navigating in Unfamiliar Geometric Terrain. In Proceedings of the Twenty-third Annual ACM Symposium on Theory of Computing, pages 494--504, 1991. To appear in SICOMP.

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A. Blum, P. Raghavan and B. Schieber, Navigating in unfamiliar geometric terrain, SIAM Journal on Computing 26 (1997), 110-137.

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A. Blum, P. Raghavan, and B. Schieber. Navigating in unfamiliar geometric terrain. SIAM Journal on Computing, 26(1):110--137, January 1997.

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A. Blum, P. Raghavan and B. Schieber, Navigating in unfamiliar geometric terrain, SIAM Journal on Computing 26 (1997), 110-137.

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A. Blum, P. Raghavan, and B. Schieber. Navigating in unfamiliar geometric terrain. SIAM J. Computing, 26(1):110--137, February 1997.

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