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An optimal algorithm for shortest paths on weighted interval and circular-arc graphs, with applications

M. J. Atallah, D. Z. Chen, D. T. Lee
1995 Algorithmica  
We give the firsl.linear-time algorithm for computing single-source shortest paths in a weighted interval or circular-arc graph, when we arc given the model of that graph, i.e" the actual weighted intervals  ...  Our algorithm solves this problem optimally in O(n) time, where n is the nUlIlber of intervals or circular-arcs in a graph. An immediate consequence of our result  ...  OUf algorithm solves this shortest paths problem on interval and circular-arc graphs optimally in O(n) time, when we are given the model of such a graph, l.e., the actual weighted intervals or circular-arcs  ... 
doi:10.1007/bf01192049 fatcat:nytfnfnntjcj5levanhlskstqi

Page 4354 of Mathematical Reviews Vol. , Issue 96g [page]

1996 Mathematical Reviews  
[Lee, Der Tsai] (1-NW-E; Evanston, IL) An optimal algorithm for shortest paths on weighted interval and circular-arc graphs, with applications.  ...  Summary: “We give the first linear-time algorithm for computing single-source shortest paths in a weighted interval or circular-arc 68 COMPUTER SCIENCE 4354 graph, when we are given the model of that graph  ... 

Page 2048 of Mathematical Reviews Vol. , Issue 99c [page]

1991 Mathematical Reviews  
Our techniques can be extended to solve the all-pair shortest path query problem on circular-arc graphs, both sequentially and in parallel, with the same complexity bounds.  ...  [Sridhar, Radhakrishnan] (1-OK-SC; Norman, OK); Sekharan, Chandra N. (1-LYLCH-CS; Chicago, IL) Solving the all-pair shortest path query problem on interval and circular-arc graphs.  ... 

Page 1457 of Mathematical Reviews Vol. , Issue 97C [page]

1997 Mathematical Reviews  
On the classes of interval and circular-arc graphs, an optimal solution to the APSL problem is available for the weighted case (Atallah et al.; 1993).  ...  As an application we also give an O(n) algorithm for qg-coloring proper circular arc graphs for a fixed g. (Such an algorithm was first given by Teng and Tucker.)  ... 

Optimizing over Consecutive 1's and Circular 1's Constraints

Dorit S. Hochbaum, Asaf Levin
2006 SIAM Journal on Optimization  
We devise here substantially more efficient and strongly polynomial algorithms based on parametric shortest paths approaches.  ...  For the "mixed" case with both covering and packing consecutive 1's constraints we present an O(mn) time algorithm.  ...  Tamir for discussing an earlier version of this paper and to anonymous referees whose comments and suggestions improved and simplified the presentation of the results in this paper.  ... 
doi:10.1137/040603048 fatcat:frlhfkp7bbbqncmnzafnyfas7i

Page 4160 of Mathematical Reviews Vol. , Issue 93h [page]

1993 Mathematical Reviews  
Summary: “Shortest path algorithms for graphs have been widely studied and are of great practical utility. For the case of a general graph, Dijkstra’s algorithm is known to be optimal.  ...  Summary: “A circular arc family F is a collection of arcs on a circle. A circular-arc graph is the intersection graph of an arc family.  ... 

Page 728 of Mathematical Reviews Vol. , Issue 85b [page]

1985 Mathematical Reviews  
From the introduction: “We consider the well-known problem of finding a shortest path between two specified nodes in a directed graph with weights on the arcs.  ...  -T. (1-NW-E) Fast algorithms for generating all maximal independent sets of interval, circular-arc and chordal graphs. J. Algorithms 5 (1984), no. 1, 22-35.  ... 

Planning Near-Optimal Corridors Amidst Obstacles [chapter]

Ron Wein, Jur van den Berg, Dan Halperin
2008 Springer Tracts in Advanced Robotics  
We analyze the structure of optimal corridors amidst point obstacles and polygonal obstacles in the plane, and propose an algorithm to compute approximations for optimal corridors according to our measure  ...  Instead of devising a one-dimensional motion path for a moving entity, it is possible to let it move in a corridor, where the exact motion path is determined by a local planner.  ...  We conclude that the optimal backbone path between s and g must contain a circular arc on the boundary of B(p; w max ).  ... 
doi:10.1007/978-3-540-68405-3_31 fatcat:6krhxnmv6zehrg6lnsxf24sdfu

Planning High-quality Paths and Corridors Amidst Obstacles

Ron Wein, Jur van den Berg, Dan Halperin
2008 The international journal of robotics research  
We analyze the structure of optimal corridors amidst point obstacles and polygonal obstacles in the plane, and propose an algorithm to compute approximations for optimal corridors according to our measure  ...  Instead of devising a one-dimensional motion path for a moving entity, it is possible to let it move in a corridor, where the exact motion path is determined by a local planner.  ...  We conclude that the optimal backbone path between s and g must contain a circular arc on the boundary of B(p; w max ).  ... 
doi:10.1177/0278364908097213 fatcat:yfmrchtwhjg6pftm6ijzpc2n5e

Page 287 of Mathematical Reviews Vol. , Issue 81A [page]

1981 Mathematical Reviews  
In this paper we present an O(n°)-step algorithm for testing whether an n-vertex graph is a circular-arc graph, and if it is, constructing a circular-arc model.  ...  As an application a new and efficient algorithm for finding the interval graph of a flow graph is derived.” {For the entire collection see MR 80m:05003.} Habib, M.; Maurer, M. C.  ... 

Sketching Clothoid Splines Using Shortest Paths

Ilya Baran, Jaakko Lehtinen, Jovan Popović
2010 Computer graphics forum (Print)  
Our main idea is to cast the segmentation as a shortest path problem on a carefully constructed weighted graph.  ...  Building on recent results, we describe a novel algorithm for approximating a sketched stroke with a fair (i.e., visually pleasing) clothoid spline.  ...  Acknowledgments We thank Tony DeRose and Mark Meyer for early discussions. Thanks to Saku Lehtinen and Daniel Vlasic for helpful feedback. Thanks to Emily Whiting for drawing some of our examples.  ... 
doi:10.1111/j.1467-8659.2009.01635.x fatcat:2wfv7laugfgmvcjwb4ta2lzktq

Page 1746 of Mathematical Reviews Vol. , Issue 95c [page]

1995 Mathematical Reviews  
[Lee, Der Tsai] (1-NW-E; Evanston, IL) An optimal algorithm for shortest paths on weighted interval and circular-arc graphs, with applications.  ...  Summary: “We give the first linear-time algorithm for computing single-source shortest paths in a weighted interval or circular-arc graph, when we are given the model of that graph, i.e., the actual weighted  ... 

Polygonal path simplification with angle constraints

Danny Z. Chen, Ovidiu Daescu, John Hershberger, Peter M. Kogge, Ningfang Mi, Jack Snoeyink
2005 Computational geometry  
We present efficient geometric algorithms for simplifying polygonal paths in R 2 and R 3 that have angle constraints, improving by nearly a linear factor over the graph-theoretic solutions based on known  ...  The algorithms we present match the time bounds for their unconstrained counterparts.  ...  Acknowledgement The authors would like to thank the anonymous reviewers for their helpful comments and suggestions.  ... 
doi:10.1016/j.comgeo.2004.09.003 fatcat:6xnshgwedvc7daebcvwjfphifa

The Routing Continuum from Shortest-Path to All-Path: A Unifying Theory

Yanhua Li, Zhi-Li Zhang, Daniel Boley
2011 2011 31st International Conference on Distributed Computing Systems  
We also develop an efficient iterative algorithm for computing the entire routing continuum.  ...  Based on the connection between routing and flow optimization in a network, in this paper we develop a unifying theoretical framework by considering flow optimization with mixed (weighted) 1/ 2-norms.  ...  Let be a path from node 1 to node . If for each edge (arc) ⟨ , ⟩ ∈ , * − * = , then is a shortest path from node 1 to node (with respect to the weights 's), and * 1 = ∑ ⟨ , ⟩∈ .  ... 
doi:10.1109/icdcs.2011.57 dblp:conf/icdcs/LiZB11 fatcat:dfoylnsx4vcazizwhkmhj5xjri

Path Planning in Dynamic Environments [chapter]

Roman Smierzchalski, Zbigniew Michalewicz
2005 Studies in Computational Intelligence  
Ferguson, and J. Kuffner. Anytime path planning and replanning in dynamic environments. In Proc. IEEE Int. Conf. on Robotics and Automation, pages 2366-2371, 2006 [16] .  ...  We already know that portions of the circular arcs that form the boundary of M are locally optimal, and that the weighted length of such a circular arc simply equals its length.  ...  We conclude that the optimal backbone path between s and g must contain a circular arc on the boundary of B(p; w max ).  ... 
doi:10.1007/10992388_4 fatcat:3ufm4h4awvdcfbbhefipt3r3kq
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