C. Papadimitriou and M. Yannakakis. Shortest paths without a map. In Proc. 16th ICALP, 1989.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....edges in both directions; however, he pays for the total distance he travels. The layered graph traversal problem belongs to a larger family of shortest path problems which operate with incomplete information about the environment being searched. It was introduced by Papadimitriou and Yannakakis [PY] and generalizes the work of Baeza Yates, Culberson and Rawlins [BCR] They [BCR, PY] consider a number of such shortest path problems and give algorithms which start at a source and search for a target, learning about the environment as they progress. The complexity measure associated with such ....

....The layered graph traversal problem belongs to a larger family of shortest path problems which operate with incomplete information about the environment being searched. It was introduced by Papadimitriou and Yannakakis [PY] and generalizes the work of Baeza Yates, Culberson and Rawlins [BCR] They [BCR, PY] consider a number of such shortest path problems and give algorithms which start at a source and search for a target, learning about the environment as they progress. The complexity measure associated with such deterministic algorithms is the worst case ratio of the total distance traversed by ....

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C.H. Papadimitriou and M. Yannakakis. Shortest paths Without a Map. In Proc. 16th ICALP, pp. 610-620, July 1989. 26

....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 ....

....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 robot so that its trips between both are as fast as can be hoped for initially, and improve as more trips are made and more information is gathered. For instance, ....

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C. Papadimitriou and M. Yannakakis. Shortest paths without a map. In Proc. 16th ICALP, 1989.

....constant factor. 1 Introduction Finding the shortest path in a graph from a source to a target is a well studied problem. Dijkstra s algorithm [Dij] appeared in 1959. Other algorithms can be found in [Bel, Flo, FF, AMOT] Baeza Yates, Culberson and Rawlins [BCR] and Papadimitriou and Yannakakis [PY] consider a large family of shortest path problems that operate with incomplete information. They describe algorithms that start at Computer Science Department, School of Mathematics, Tel Aviv University, Tel Aviv 69978, Israel. University of Pennsylvania, Department of Statistics, The ....

....the cost of A on oe a constant additive term is subtracted, before dividing by the cost of ADV on oe. Where ambiguity might arise, we shall say that A is strictly c competitive, meaning that the definition without an additive term is used. The layered graph traversal problem was introduced in [PY], and generalizes work of [BCR] A layered graph is a connected graph in which the vertices are partitioned into sets L 0 = fsg; L 1 ; L 2 ; L 3 ; and all edges run between L i Gamma1 and L i for some i. Each edge has a nonnegative integral weight. Vertex s is known as the source. Let w = ....

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C.H. Papadimitriou and M. Yannakakis. Shortest Paths Without a Map. In Proc. 16th ICALP, pages 610--620, July 1989.

....the robot sees new parts of it, and the goal is (in general) to minimize the total distance traveled. The recent incorporation of navigation problems into the setting of competitive analysis comes mainly from the work of Baeza Yates, Culberson, and Rawlins [BCR] and Papadimitriou and Yannakakis [PY]. BCR] does not speak directly in terms of the competitive ratio, but its focus on the ratio of the robot s distance traveled to the length of the shortest path is clear enough. The questions it considers are variations on the theme of searching for an object at an unknown location in the plane ....

....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 ....

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C. Papadimitriou, M. Yannakakis, "Shortest paths without a map," Theoretical Computer Science, 84(1991), pp. 127--150.

....criteria: maximin [46] minmax regret and competitive ratio. The rst two criteria are well known in the decision theory literature [36, 38] while competitive ratio is used in the theoretical computer science literature as the primary optimization measure for on line algorithms (see, e.g. [4, 39]) A central property in all these results is that of closure under union: if an agent prefers action a over b given that the possible worlds are s 1 and s 2 and she prefers a over b when the possible worlds are s 3 and s 4 , then she still prefers a over b when the possible worlds are s 1 ; s 2 ; ....

....to some extent, as we discuss in Section 7. The main motivation for our study is the foundations of qualitative decision theory, but our results have two additional interesting rami cations. First, the competitive ratio decision criterion plays a major role in the analysis of on line algorithms [4, 39]. Hence, our representation theorems for this criterion should be relevant to the foundations of research in that area. Second, our results show how certain agents behaviors can be represented compactly: There are di erent ways in which we can encode an agent s behavior (or pro3 gram) One ....

[Article contains additional citation context not shown here]

C.H. Papadimitriou and M. Yannakakis. Shortest Paths Without a Map. In Automata, Languages and Programming. 16th International Colloquium Proceedings, pages 610{ 620, 1989.

....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 ....

C. H. Papadimitriou and M. Yannakakis. Shortest paths without a map. In Proc. 16th Internat. Colloq. Automata Lang. Program., volume 372 of Lecture Notes in Computer Science, pages 610-620. Springer-Verlag, 1989.

....of the problem in which the values of link weight and delay functions become known only upon an arrival to a vertices or a link, and their future values are unknown. Very few studies of the on line variant of the problem exist. One special case is known as the Canadian Traveler Problem [12] [13]. In this problem a certain finite number of link failures (modeled by infinite link weights) may occur with failed links either remaining faulty forever, or being recovered after a finite period of time, recovery time. A strictly positive constant delay is associated with every link when it is ....

C.H. Papadimitriou and M. Yannakakis, "Shortest paths without a map," in 16th ICALP, July 1989.

....criteria: maximin [46] minmax regret and competitive ratio. The first two criteria are well known in the decision theory literature [36, 38] while competitive ratio is used in the theoretical computer science literature as the primary optimization measure for on line algorithms (see, e.g. [4, 39]) A central property in all these results is that of closure under union: if an agent prefers action a over b given that the possible worlds are s 1 and s 2 and she prefers a over b when the possible worlds are s 3 and s 4 , then she still prefers a over b when the possible worlds are s 1 ; s 2 ; ....

....to some extent, as we discuss in Section 7. The main motivation for our study is the foundations of qualitative decision theory, but our results have two additional interesting ramifications. First, the competitive ratio decision criterion plays a major role in the analysis of on line algorithms [4, 39]. Hence, our representation theorems for this criterion should be relevant to the foundations of research in that area. Second, our results show how certain agents behaviors can be represented compactly: There are different ways in which we can encode an agent s behavior (or pro3 gram) One ....

[Article contains additional citation context not shown here]

C.H. Papadimitriou and M. Yannakakis. Shortest Paths Without a Map. In Automata, Languages and Programming. 16th International Colloquium Proceedings, pages 610-- 620, 1989.

....edge e i is blocked, then the edge cannot be traversed. We are given a start vertex s and a target vertex t, where s; t 2 V . Also let jV j = n and jEj = m. In this paper, we use the notion of a traveler in a network of roads. This notion follows from the canadian traveler s problem discussed in [7]. In the case where the graph being considered is a set of network links, the traveler will be a packet in the network. A strategy r to reach the vertex t from s is a function f : P E, where P is the set of all possible paths that the traveler can traverse, and E is the set of all edges in G. ....

C. H. Papadimitriou and M. Yannakakis, "Shortest Paths without a Map", Theoretical Computer Science, vol 84, 1991, pp 127 - 50

....Widom [3] considered the selection problem, with median as a special case, for both the offline and online formulations. Finally, Khanna and Tan [6] extended some of the results for the selection and sum problems, focusing on alternative precision parameter formulations. Papadimitriou and others [9, 10] study problems related to the online problem described earlier; in their model, a robot tries to discover the map of a two or three dimensional Euclidian area for a cost competitive with that of the cheapest witness to the map structure. Here cost is the total distance the robot travels to ....

C. H. Papadimitriou and M. Yannakakis. "Shortest paths without a map." In Proceedings of the 16th International Colloquium on Automata, Languages, and Programming, Lecture Notes in Computer Science vol. 372 (1989) 610--620.

....where a learner, to perform a task better, must learn a complete map of its environment. For example, the learner might be a security guard robot, a taxi driver, or a trail guide. Exploration of unknown environments has been addressed by many previous authors, such as Papadimitriouand Yanakakis [10], Blum, Raghavan, and Schieber [4] Rivest and Schapire [12] Deng and Papadimitriou [7] Betke [3] Deng, Kameda, and Papadimitriou [6] Rao, Kareti, Shi and Iyengar [11] and Bar Eli, Berman, Fiat, and Yan [2] This paper considers a new constraint: for some reason learning must be done ....

....rectangles whose opposing 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 1 gives an example. City block graphs are also studied by Papadimitriou and Yanakakis [10], Blum, Raghavan, and Schieber [4] and Bar Eli, Berman, Fiat and Yan [2] 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 ....

Papadimitriou, Christos H. and M. Yanakakis. "Shortest paths without a map," Theoretical Computer Science, volume 84, 1991, pp. 127--150.

.... [14] various mobile robot navigation problems in which environments possess detectable state, such as doors that might be open or closed [3] and graph theoretical problems such as the Canadian Travelers Problem, which is the problem of traveling through a graph where edges might be unpassable [10]. We propose a heuristic search algorithm for finding optimal policies in MDPDHSs. Our approach performs heuristic search in the space of all information states, similar to approaches popular in the POMDP literature [5] but in a discrete way. The primary algorithmic contribution of this paper is ....

....end. Arcs in the graph might or might not be traversable, but the only way to find out is to move there and try. The problem is to find an optimal contingency plan that enables the agent to recover is an arc is found to be impassable. This problem is known as the NP hard Canadian Travelers Problem [10], and is very similar to the mobile robot exploration problem [13] The advantage of an artificial environment such as the one used here is that it complexity can easily be varied, by adding new nodes to the graph. The number of arcs, and hence the number of hidden states, is linear in the number ....

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C. Papadimitriou and M. Yannakakis. Shortest paths without a map. ICALP-89.

....In view of the example in Fig. 1 our strategy is optimal up to a constant factor and, hence, settles the asymptotic complexity of on line robot localization in trees, thus solving an open problem posed by Kleinberg. Another important problem in robotics is searching for a target in an environment [2, 3, 4, 5, 6, 10, 14]. If a map of the environment and the position of the target on the map are given, but the robot s position on the map is not given, then Fig. 1 again provides an example of an Omega Gamma p n) lower bound for the competitive ratio of an on line strategy. We show that our approach can be used ....

C. H. Papadimitriou and M. Yannakakis. Shortest paths without a map. Theoret. Comput. Sci., 84(1):127--150, 1991.

....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 ....

C. H. Papadimitriou and M. Yannakakis. Shortest paths without a map. In Proc. 16th Internat. Colloq. Automata Lang. Program., volume 372 of Lecture Notes in Computer Science, pages 610-620. Springer-Verlag, 1989.

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C. Papadimitriou and M. Yannakakis. Shortest paths without a map. In Proc. 16th ICALP, 1989.

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Papadimitriou, C. H., and Yannakakis, M. (1989), Shortest paths without a map, Theoretical Comput. Sci. 84, pp. 127--150.

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C. H. Papadimitriou and M. Yannakakis. Shortest paths without a map. Theoret. Comput. Sci., 84(1):127--150, 1991.

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C. PAPADIMITRIOU AND M. YANNAKAKIS, Shortest paths without a map, Theoret. Comput. Sci., 84 (1991), pp. 127--150.

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P. Papadimitriou and M. Yannakakis. Shortest paths without a map. In Int. Colloq. on Automata, Languages, and Programming (ICALP 89), 1989.

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C.H. Papadimitriou and M. Yannakakis. "Shortest paths without a map." In Proceedings of the 16th International Colloquium on Automata, Languages, and Programming, Lecture Notes in Computer Science 372(1989):610--620.

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C.H. Papadimitriou and M. Yannakakis. Shortest Paths without a Map. In 16th ICALP, pages 610-620, July 1989.

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C. Papadimitriou and M. Yanakakis, "Shortest paths without a map," Proceedings of the 16th ICALP, 1989, pp. 610-620.

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C. H. Papadimitriou and M. Yannakakis. Shortest paths without a map. In 16th International Colloquium on Automata, Languages, and Programming, Lecture Notes in Computer Science vol. 372, pages 610--620. Springer-Verlag, 1989.

No context found.

C.H. Papadimitriou and M. Yannakakis, "Shortest paths without a map," in 16th ICALP, July 1989.

No context found.

C. H. Papadimitriou and M. Yannakakis. Shortest paths without a map. Theoret. Comput. Sci., 84(1):127--150, 1991.

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