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Shortest paths among obstacles in the plane

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Joseph S. B. MitchellAuthors Info & Claims

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

Pages 308 - 317

https://doi.org/10.1145/160985.161156

Published: 01 July 1993 Publication History

Abstract

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 visibility graphs, relying instead on the continuous Dijkstra paradigm. The output is a shortest path map (of size O(n)) with respect to a given source point, which allows shortest path length queries to be answered in time O(log n). The algorithm extends to the case of multiple source points, yielding a geodesic Voronoi diagram within the same time bound.

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Cited By

Ibrahim IGillis JDecré WSwevers J(2024)Exact Wavefront Propagation for Globally Optimal One-to-All Path Planning on 2D Cartesian GridsIEEE Robotics and Automation Letters10.1109/LRA.2024.34604099:11(9431-9437)Online publication date: Nov-2024
https://doi.org/10.1109/LRA.2024.3460409
Sharma RKallmann M(2023)Computing and analyzing decision boundaries from shortest path mapsComputers and Graphics10.1016/j.cag.2023.10.006117:C(73-84)Online publication date: 1-Dec-2023
https://dl.acm.org/doi/10.1016/j.cag.2023.10.006
Zhuang JLuo JLiu Y(2020)A Locking Sweeping Method Based Path Planning for Unmanned Surface Vehicles in Dynamic Maritime EnvironmentsJournal of Marine Science and Engineering10.3390/jmse81108878:11(887)Online publication date: 7-Nov-2020
https://doi.org/10.3390/jmse8110887
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Index Terms

Shortest paths among obstacles in the plane
1. Mathematics of computing
  1. Discrete mathematics
    1. Graph theory
      1. Paths and connectivity problems
2. Theory of computation
  1. Randomness, geometry and discrete structures
    1. Computational geometry

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cover image ACM Conferences

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

July 1993

406 pages

ISBN:0897915828

DOI:10.1145/160985

Chairman:
Chee Yap

Copyright © 1993 ACM.

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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Publication History

Published: 01 July 1993

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9SCG93: Ninth Symposium on Computational Geometry

May 18 - 21, 1993

California, San Diego, USA

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

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Cited By

Ibrahim IGillis JDecré WSwevers J(2024)Exact Wavefront Propagation for Globally Optimal One-to-All Path Planning on 2D Cartesian GridsIEEE Robotics and Automation Letters10.1109/LRA.2024.34604099:11(9431-9437)Online publication date: Nov-2024
https://doi.org/10.1109/LRA.2024.3460409
Sharma RKallmann M(2023)Computing and analyzing decision boundaries from shortest path mapsComputers and Graphics10.1016/j.cag.2023.10.006117:C(73-84)Online publication date: 1-Dec-2023
https://dl.acm.org/doi/10.1016/j.cag.2023.10.006
Zhuang JLuo JLiu Y(2020)A Locking Sweeping Method Based Path Planning for Unmanned Surface Vehicles in Dynamic Maritime EnvironmentsJournal of Marine Science and Engineering10.3390/jmse81108878:11(887)Online publication date: 7-Nov-2020
https://doi.org/10.3390/jmse8110887
Farias RKallmann M(2020)Optimal Path Maps on the GPUIEEE Transactions on Visualization and Computer Graphics10.1109/TVCG.2019.290427126:9(2863-2874)Online publication date: 1-Sep-2020
https://doi.org/10.1109/TVCG.2019.2904271
Maheshwari ANouri ASack J(2020)Shortest paths among transient obstaclesJournal of Combinatorial Optimization10.1007/s10878-020-00604-143:5(1036-1074)Online publication date: 7-Jul-2020
https://doi.org/10.1007/s10878-020-00604-1
Sinyukov DPadir T(2019)CWave: Theory and Practice of a Fast Single-source Any-angle Path Planning AlgorithmRobotica10.1017/S0263574719000560(1-28)Online publication date: 15-May-2019
https://doi.org/10.1017/S0263574719000560
Maheshwari ANouri ASack J(2018)Rectilinear Shortest Paths Among Transient ObstaclesCombinatorial Optimization and Applications10.1007/978-3-030-04651-4_2(19-34)Online publication date: 16-Nov-2018
https://doi.org/10.1007/978-3-030-04651-4_2
Palachano NAllbeck JKapadia MBadler N(2016)Efficient and Flexible Navigation Meshes for Virtual WorldsSimulating Heterogeneous Crowd with Interactive Behaviors10.1201/9781315370071-3(25-42)Online publication date: 19-Oct-2016
https://doi.org/10.1201/9781315370071-3
Kallmann MKapadia M(2016)Geometric and discrete path planning for interactive virtual worldsACM SIGGRAPH 2016 Courses10.1145/2897826.2927310(1-29)Online publication date: 24-Jul-2016
https://dl.acm.org/doi/10.1145/2897826.2927310
Oyler DGirard A(2016)Dominance regions in the Homicidal Chauffeur Problem2016 American Control Conference (ACC)10.1109/ACC.2016.7525291(2494-2499)Online publication date: Jul-2016
https://doi.org/10.1109/ACC.2016.7525291
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