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

1995
*
Algorithmica
*

We give the firsl.linear-time

doi:10.1007/bf01192049
fatcat:nytfnfnntjcj5levanhlskstqi
*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*...##
###
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

2006
*
SIAM Journal on Optimization
*

We devise here substantially more efficient

doi:10.1137/040603048
fatcat:frlhfkp7bbbqncmnzafnyfas7i
*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. ...##
###
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]

2008
*
Springer Tracts in Advanced Robotics
*

We analyze the structure of

doi:10.1007/978-3-540-68405-3_31
fatcat:6krhxnmv6zehrg6lnsxf24sdfu
*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 ). ...##
###
Planning High-quality Paths and Corridors Amidst Obstacles

2008
*
The international journal of robotics research
*

We analyze the structure of

doi:10.1177/0278364908097213
fatcat:yfmrchtwhjg6pftm6ijzpc2n5e
*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 ). ...##
###
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

2010
*
Computer graphics forum (Print)
*

Our main idea is to cast the segmentation as a

doi:10.1111/j.1467-8659.2009.01635.x
fatcat:2wfv7laugfgmvcjwb4ta2lzktq
*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. ...##
###
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

2005
*
Computational geometry
*

We present efficient geometric

doi:10.1016/j.comgeo.2004.09.003
fatcat:6xnshgwedvc7daebcvwjfphifa
*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. ...##
###
The Routing Continuum from Shortest-Path to All-Path: A Unifying Theory

2011
*
2011 31st International Conference on Distributed Computing Systems
*

We also develop

doi:10.1109/icdcs.2011.57
dblp:conf/icdcs/LiZB11
fatcat:dfoylnsx4vcazizwhkmhj5xjri
*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 = ∑ ⟨ , ⟩∈ . ...##
###
Path Planning in Dynamic Environments
[chapter]

2005
*
Studies in Computational Intelligence
*

Ferguson,

doi:10.1007/10992388_4
fatcat:3ufm4h4awvdcfbbhefipt3r3kq
*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 ). ...
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