J. S. B. Mitchell. Geometric shortest paths and network optimization. In J.-R. Sack and J. Urrutia, editors, Handbook of Computational Geometry, page ?? Elsevier Science Publishers B.V. North-Holland, Amsterdam, 1998. Home/Search Document Details and Download
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On the Competitive Complexity of Navigation Tasks - Icking, Kamphans, Klein.. (2002) (Correct)
....the robot has to search for the target in a systematic way. Only with luck will it discover t immediately; in general, when the robot eventually arrives at t, its path will be more expensive than the optimum path from s to t. Our interest is in keeping the extra cost See e.g. the survey article [37] for e#cient algorithms for computing shortest paths in known two dimensional environments. G.D. Hager et al. Eds. Sensor Based Intelligent Robots, LNCS 2238, pp. 245 258, 2002. c Springer Verlag Berlin Heidelberg 2002 246 Christian Icking et al. as small as possible, by designing a ....
....4.44, Kleinberg [28] 2.61, Lopez Ortiz and Schuierer [31] 2.05, Lopez Ortiz and Schuierer [33] 1.73, Semrau [41] 1.57, Icking et al. 24] 1. 51, Dasgupta et al. 10] Kranakis and Spatharis [29] Lopez Ortiz and Schuierer [34] The gap between the upper and lower bound, also mentioned in Mitchell [37], was finally closed by Icking et al. 22] and independently by Semrau and Schuierer [40] A java implementation of this strategy is available at http: www.informatik.uni bonn.de I GeomLab Gridrobot . t r # s v l v r lr t l # 0 Fig. 1. A funnel. 2.2 Funnels The competitive ....
J. S. B. Mitchell. Geometric shortest paths and network optimization. In J.-R. Sack and J. Urrutia, editors, Handbook of Computational Geometry, pages 633--701. Elsevier Science Publishers B.V. North-Holland, Amsterdam, 2000.
Computing Homotopic Shortest Paths Efficiently - Efrat, Kobourov, Lubiw (Correct)
....Our deterministic algorithm runs in time O(k log n n # n) and the randomized version in time O(k log n n(log n) where k is the input plus output sizes of the paths. 1 Introduction Geometric shortest paths are a major topic in computational geometry; see the survey paper by Mitchell [15]. A shortest path between two points in a simple polygon can be found in linear time using the funnel algorithm of Chazelle [3] and Lee and Preparata [13] A more general problem is to find a shortest path between two points in a polygonal domain. In this case the rubber band solution is not ....
....the rubber band solution is not unique, or, to put it another way, di#erent paths may have di#erent homotopy types. When the homotopy type of the solution is not specified, there are two main approaches, the visibility graph approach, and the continuous Dijkstra (or shortest path map) approach [15]. In this paper, we address the problem of finding a shortest path when the homotopy type is specified. Colloquially, we have a sketch of how the path should wind its way among the obstacles, and we want to pull the path tight to shorten it. Homotopic shortest paths are used in VLSI routing ....
J. S. B. Mitchell. Geometric shortest paths and network optimization. In J.-R. Sack and J. Urrutia, editors, Handbook of Computational Geometry. 1998.
On Finding Approximate Optimal Paths in Weighted Regions - Sun, Reif (Correct)
....or 3D space under various conditions. Due to their practical signi cance, these problems have drawn great attention from researchers in robotics as well as other areas such as computational geometry, geographical information systems (GIS) and graph theory. Interested readers may refer to survey [10] for a comprehensive review of the previous works on these problems. In this paper we study the 2D weighted region optimal path problem. In this problem, a 2D space is divided into n triangular regions, each of which is associated with a distinct positive unit weight. Such a space can be used to ....
.... Comparison Algorithm Complexity Error Mitchell and Papadimitriou [11] O(n Lanthier et al. 7] O(n O(Lwmax ) absolute Lanthier et al. 7] O( log n) relative and O(Lwmax ) absolute Mata and Mitchell [9] O( For other related work, see [3, 4, 5, 6, 12, 13, 15, 16] or see survey [10]. 2 Preliminaries 2.1 Notations Let S be a planar space consisting of n triangular regions. We use V and E to denote the set of vertices and the set of boundary edges, respectively, of all regions. Therefore, jV j = O(n) and jEj = O(n) For any region r, we use w r to denote the unit weight of ....
J. S. B. Mitchell. Geometric shortest paths and network optimization. In J.-R. Sack and J. Urrutia, editors, Handbook of Computational Geometry, pages 633-701. Elsevier Science Publishers B.V. NorthHolland, Amsterdam, 2000.
Adaptive and Compact Discretization for Weighted Region Optimal.. - Sun, Reif (Correct)
....contain optimal paths. BUSHWHACK is a discrete search algorithm used for nding optimal paths in G . We added two heuristics to BUSHWHACK to improve its performance and scalability. 1 Introduction In the past two decades the geometric optimal path problems have been extensively studied (see [1] for a review) These problems have a wide range of applications in robotics and geographical information systems. In this paper we study the path planning problem for a point robot in a 2D space consisting of n triangular regions, each of which is associated with a distinct unit weight. Such a ....
Mitchell, J.S.B.: Geometric shortest paths and network optimization. In Sack, J.R., Urrutia, J., eds.: Handbook of Computational Geometry. Elsevier Science Publishers B.V. North-Holland, Amsterdam (2000) 633-701
Movement Planning in the Presence of Flows - John Reif Zheng (2001) (Correct)
....results for robotic motion with moving obstacles (also see Wilfong [19] Canny and Reif [4] showed the 3D minimal cost path problem with polygonal obstacles is NP hard, and Reif and Storer [15] applied the theory of real closed elds to give a decision algorithm for this problem. The reference [8] surveys work on the 2D and 3D minimal cost path problem, and approximation algorithms for the weighted region minimal cost path problem include the continuous Dijkstra method of Mitchell and Papadimitriou [9] as well as a variety of other discretization algorithms given by Mata and Mitchell [7] ....
J. S. B. Mitchell. Geometric shortest paths and network optimization. In Jorg-Rudiger Sack and Jorge Urrutia, editors, Handbook of Computational Geometry. Elsevier Science Publishers B.V. North-Holland, Amsterdam, 1998.
A Shortest Path Algorithm for Real-Weighted Undirected Graphs - Pettie, Ramachandran (2002) (Correct)
....of Pettie [Pet02a, Pet02b] Dijkstra s algorithm [Dij59, J77, FT87] was also the best for computing APSP on sparse graphs. In order to improve these bounds most shortest path algorithms depend on a restricted type of input. There are algorithms for geometric inputs (see Mitchell s survey [M00]) planar graphs [F91, H 97, FR01] and graphs with randomly chosen edge weights [S73, FG85, MT87, KKP93, KS98, M01, G01] In recent years there has also been a focus on computing approximate shortest paths see Zwick s recent survey [Z01] One common assumption is that the graph is ....
J. S. B. Mitchell. Geometric shortest paths and network optimization. Handbook of computational geometry, 633-701, North-Holland, Amsterdam, 2000.
Adaptive and Compact Discretization for Weighted Regions Optimal .. - Sun, Reif (Correct)
....contain optimal paths. BUSHWHACK is a discrete search algorithm used for finding optimal paths in # . We added two heuristics to BUSHWHACK to improve its performance and scalability. 1 Introduction In the past two decades the geometric optimal path problems have been extensively studied (see [5] for a review) These problems have a wide range of applications in robotics and geographical information systems. In this paper we study the weighted region optimal path problem, where the 2D space consists of n triangular regions with di#erent unit weights, and the goal is to find between given ....
J. S. B. Mitchell. Geometric shortest paths and network optimization. In JorgR udiger Sack and Jorge Urrutia, editors, Handbook of Computational Geometry, pages 633--701. Elsevier Science Publishers B.V. North-Holland, Amsterdam, 2000.
Algorithms for Rapidly Dispersing Robot Swarms in.. - Hsiang, Arkin.. (2002) (1 citation) Self-citation (Mitchell) (Correct)
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J. S. B. Mitchell, Geometric shortest paths and network optimization, In Handbook of Computational Geometry (J.-R. Sack and J. Urrutia, editors), pages 633-701. Elsevier Science Publishers B.V. North-Holland, Amsterdam, 2000.
Touring a Sequence of Polygons - Dror, Efrat, Lubiw, Mitchell (2003) (1 citation) Self-citation (Mitchell) (Correct)
....same as the starting point s, we are computing a shortest cycle ( tour ) through s visiting the P i s. If the order in which the polygons P i must be visited is not specified, then the touring polygons problem becomes the Traveling Salesperson Problem with Neighborhoods, which is NP hard. See [20]. The touring polygons problem can be modeled as a special kind of 3 dimensional shortest path problem among polyhedral obstacles. Imagine k very large sheets of paper stacked up in parallel planes orthogonal to the z axis. The i th sheet has a hole, P i , cut out of it; each sheet of paper is a ....
J. S. B. Mitchell, Geometric shortest paths and network optimization, In Handbook of Computational Geometry (J.-R. Sack and J. Urrutia, eds.), pages 633--701, Elsevier Science, 2000.
Two-Point Euclidean Shortest Path Queries in the Plane - Exte Nd Ed (Correct)
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J. S. B. Mitchell. Geometric shortest paths and network optimization. In J.-R. Sack and J. Urrutia, editors, Handbook of Computational Geometry, page ?? Elsevier Science Publishers B.V. North-Holland, Amsterdam, 1998.
Randolphs Robot Game is NP-complete! - Engels, Kamphans (2006) (Correct)
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J. S. B. Mitchell. Geometric shortest paths and network optimization. In J.-R. Sack and J. Urrutia, editors, Handbook of Computational Geometry, pages 633--701. Elsevier Science Publishers B.V. North-Holland, Amsterdam, 2000.
On the Complexity of Randolph's Robot Game - Engels, Kamphans (2005) (Correct)
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J. S. B. Mitchell. Geometric shortest paths and network optimization. In J.-R. Sack and J. Urrutia, editors, Handbook of Computational Geometry, pages 633--701. Elsevier Science Publishers B.V. North-Holland, Amsterdam, 2000.
Competitive Online Searching for a Ray in the Plane - Andrea Eubeler Rudolf (Correct)
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J. S. B. Mitchell. Geometric shortest paths and network optimization. In J.-R. Sack and J. Urrutia, editors, Handbook of Computational Geometry, pages 633--701. Elsevier Science Publishers B.V. North-Holland, Amsterdam, 2000.
The Pledge Algorithm Reconsidered under Errors in Sensors.. - Kamphans, Langetepe (2004) (Correct)
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J. S. B. Mitchell. Geometric shortest paths and network optimization. In J.-R. Sack and J. Urrutia, editors, Handbook of Computational Geometry, pages 633--701. Elsevier Science Publishers B.V. North-Holland, Amsterdam, 2000.
Optimal Competitive Online Ray Search with an Error-Prone Robot - Tom Kamphans And (2005) (Correct)
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J. S. B. Mitchell. Geometric shortest paths and network optimization. In J.-R. Sack and J. Urrutia, editors, Handbook of Computational Geometry, pages 633--701. Elsevier Science Publishers B.V. North-Holland, Amsterdam, 2000.
Leaving an Unknown Maze Using an Error-Prone Compass - Kamphans, Langetepe (2006) (Correct)
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J. S. B. Mitchell. Geometric shortest paths and network optimization. In J.-R. Sack and J. Urrutia, editors, Handbook of Computational Geometry, pages 633--701. Elsevier Science Publishers B.V. North-Holland, Amsterdam, 2000.
Exploring Simple Grid Polygons - Icking, Kamphans, Klein, Langetepe (2005) (Correct)
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J. S. B. Mitchell. Geometric shortest paths and network optimization. In J.-R. Sack and J. Urrutia, editors, Handbook of Computational Geometry, pages 633-- 701. Elsevier Science Publishers B.V. North-Holland, Amsterdam, 2000.
Exploring Grid Polygons Online - Icking, Kamphans, Klein, Langetepe (2005) (Correct)
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J. S. B. Mitchell. Geometric shortest paths and network optimization. In J.-R. Sack and J. Urrutia, editors, Handbook of Computational Geometry, pages 633--701. Elsevier Science Publishers B.V. North-Holland, Amsterdam, 2000.
D Rectilinear Motion Planning with Minimum Bend Paths - Robert Fitch Zack (Correct)
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J.S.B. Mitchell. Geometric shortest paths and network optimization. In J.R. Sack and J. Urrutia, editors, Science Publishers B.V. NorthHolland, Amsterdam, 2000.
Efficient Optimal Search of Euclidean-Cost Grids and Lattices - Kuffner (2004) (Correct)
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J. Mitchell, Handbook of Computational Geometry. Elsevier Science, 1998, ch. Geometric Shortest Paths and Network Optimization.
Geometric Analysis Of Cross-Linkability - For Protein Fold (Correct)
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J. S. B. Mitchell. Geometric shortest paths and network optimization. Handbook of Computational Geometry, 2000.
Transportation Voronoi Diagrams - Yaron Ostrovksy-Berman School (2003) (Correct)
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J. S. B. Mitchell. Geometric shortest paths and network optimization. In J.-R. Sack and J. Urrutia, editors, Handbook of Computational Geometry, pages 633--701. Elsevier Science Publishers B.V. North-Holland, Amsterdam, 2000.
Exact and Approximate Distances in Graphs - a survey - Zwick (2001) (8 citations) (Correct)
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J.S.B. Mitchell. Geometric shortest paths and network optimization. In JorgR udiger Sack and Jorge Urrutia, editors, Handbook of Computational Geometry, pages 633-701. Elsevier Science Publishers B.V. North-Holland, Amsterdam, 2000.
Algorithmique des Graphes de Visibilité - ANGELIER (2002) (Correct)
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Joseph S. B. Mitchell. Geometric shortest paths and network optimization. In Jrg-Rdiger Sack and Jorge Urrutia, editors, Handbook of Computational Geometry, pages 633701. Elsevier Science Publishers B.V. North-Holland, Amsterdam, 2000.
On the Complexity of Approximating TSP with Neighborhoods and .. - Safra, Schwartz (Correct)
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Joseph S. B. Mitchell. Geometric Shortest Paths and Network optimization. Elsevier Science, preliminary edition, 2000.
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