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Minimum-link paths among obstacles in the plane

Authors:

Joseph S. B. Mitchell,

Günter Rote,

Gerhard WoegingerAuthors Info & Claims

SCG '90: Proceedings of the sixth annual symposium on Computational geometry

Pages 63 - 72

https://doi.org/10.1145/98524.98537

Published: 01 May 1990 Publication History

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Abstract

Given a set of nonintersecting polygonal obstacles in the plane, the link distance between two points s and t is the minimum number of edges required to form a polygonal path connecting s to t that avoids all obstacles. We present an algorithm that computes the link distance (and a corresponding minimum-link path) between two points in time Ο(Eα(n) log² n) (and space Ο(E)), where n is the total number of edges of the obstacles, E is the size of the visibility graph, and α(n) denotes the extremely slowly growing inverse of Ackermann's function.

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Cited By

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Bitner SCheung YCook ADaescu OKurdia AWenk C(2010)Visiting a sequence of points with a bevel-tip needleProceedings of the 9th Latin American conference on Theoretical Informatics10.1007/978-3-642-12200-2_43(492-502)Online publication date: 19-Apr-2010
https://dl.acm.org/doi/10.1007/978-3-642-12200-2_43
Shih F(2010)Distance Transformation and Shortest Path PlanningImage Processing and Pattern Recognition10.1002/9780470590416.ch6(179-218)Online publication date: 4-Aug-2010
https://doi.org/10.1002/9780470590416.ch6
Cook AWenk C(2009)Link Distance and Shortest Path Problems in the PlaneProceedings of the 5th International Conference on Algorithmic Aspects in Information and Management10.1007/978-3-642-02158-9_13(140-151)Online publication date: 18-Jun-2009
https://dl.acm.org/doi/10.1007/978-3-642-02158-9_13
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Minimum-link paths among obstacles in the plane

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SCG '93: Proceedings of the ninth annual symposium on Computational geometry

We give a subquadratic (O(n^5/3+ε) time and space) algorithm for computing Euclidean shortest paths in the plane in the presence of polygonal obstacles; previous time bounds were at least quadratic in n, in the worst-case. The method avoids use of ...
Minimum-link paths among obstacles in the plane
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Given a set of nonintersecting polygonal obstacles in the plane, thelink distance between two pointss andt is the minimum number of edges required to form a polygonal path connectings tot that avoids all obstacles. We present an algorithm that ...
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Published In

SCG '90: Proceedings of the sixth annual symposium on Computational geometry

May 1990

371 pages

ISBN:0897913620

DOI:10.1145/98524

Chairman:
Raimund Seidel

Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than ACM must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from [email protected]

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Association for Computing Machinery

New York, NY, United States

Publication History

Published: 01 May 1990

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SOCG

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SOCG: 6th Annual Conference on Computational Geometry

June 7 - 9, 1990

California, Berkley, USA

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Overall Acceptance Rate 625 of 1,685 submissions, 37%

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Cited By

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Bitner SCheung YCook ADaescu OKurdia AWenk C(2010)Visiting a sequence of points with a bevel-tip needleProceedings of the 9th Latin American conference on Theoretical Informatics10.1007/978-3-642-12200-2_43(492-502)Online publication date: 19-Apr-2010
https://dl.acm.org/doi/10.1007/978-3-642-12200-2_43
Shih F(2010)Distance Transformation and Shortest Path PlanningImage Processing and Pattern Recognition10.1002/9780470590416.ch6(179-218)Online publication date: 4-Aug-2010
https://doi.org/10.1002/9780470590416.ch6
Cook AWenk C(2009)Link Distance and Shortest Path Problems in the PlaneProceedings of the 5th International Conference on Algorithmic Aspects in Information and Management10.1007/978-3-642-02158-9_13(140-151)Online publication date: 18-Jun-2009
https://dl.acm.org/doi/10.1007/978-3-642-02158-9_13
Stifter S(2005)Shortest non-synchronized motions parallel versions for shared memory crew modelsParallel Computation10.1007/3-540-57314-3_8(87-104)Online publication date: 29-May-2005
https://doi.org/10.1007/3-540-57314-3_8
Lee D(2005)Rectilinear paths among rectilinear obstaclesAlgorithms and Computation10.1007/3-540-56279-6_53(5-20)Online publication date: 9-Jun-2005
https://doi.org/10.1007/3-540-56279-6_53
Berg MKreveld MNilsson BOvermars M(2005)Finding shortest paths in the presence of orthogonal obstacles using a combined L 1 and link metricSWAT 9010.1007/3-540-52846-6_91(213-224)Online publication date: 8-Jun-2005
https://doi.org/10.1007/3-540-52846-6_91
Yang CLee DWong C(1997)The Smallest Pair of Noncrossing Paths in a Rectilinear PolygonIEEE Transactions on Computers10.1109/12.60928046:8(930-941)Online publication date: 1-Aug-1997
https://dl.acm.org/doi/10.1109/12.609280
Stifter S(1997)Optimal Collision Free Path Planning for Non-Synchronized MotionsJournal of Intelligent and Robotic Systems10.1023/A:100798202342719:2(187-205)Online publication date: 1-Jun-1997
https://dl.acm.org/doi/10.1023/A%3A1007982023427
Sellen J(1995)Direction weighted shortest path planningProceedings of 1995 IEEE International Conference on Robotics and Automation10.1109/ROBOT.1995.525552(1970-1975)Online publication date: 1995
https://doi.org/10.1109/ROBOT.1995.525552
Goodrich M(1995)Efficient piecewise-linear function approximation using the uniform metricDiscrete & Computational Geometry10.1007/BF0257071714:4(445-462)Online publication date: 1-Dec-1995
https://dl.acm.org/doi/10.1007/BF02570717
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Shortest paths among obstacles in the plane