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Path planning in 0/1/ weighted regions with applications

Authors:

J. S. Mitchell,

S. NtafosAuthors Info & Claims

SCG '88: Proceedings of the fourth annual symposium on Computational geometry

Pages 266 - 278

https://doi.org/10.1145/73393.73421

Published: 06 January 1988 Publication History

Abstract

We consider the terrain navigation problem in a two-dimensional polygonal subdivision consisting of obstacles, “free” regions (in which one can travel at no cost), and regions in which cost is proportional to distance traveled. This problem is a special case of the weighted region problem and is a generalization of the well-known planar shortest path problem in the presence of obstacles. We present an Ο(n²) exact algorithm for this problem and faster algorithms for the cases of convex free regions and/or obstacles. We generalize our algorithm to allow arbitrary weights on the edges of the subdivision. In addition, we present algorithms to solve a variety of important applications: (1) an Ο(n²W) algorithm for finding lexicographically shortest paths in weighted regions (with W different weights); (2) an Ο(k²n²) algorithm for planning least-risk paths in a simple polygon that contains k line-of-sight threats (this becomes Ο(k⁴n⁴) in polygons with holes); and (3) an Ο(k²n³) algorithm for finding least-risk watchman routes in simple rectilinear polygons (a watchman route is such that each point in the polygon is visible from at least one point along the route).

References

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Farias RKallmann M(2020)Planar max flow maps and determination of lanes with clearanceAutonomous Robots10.1007/s10514-020-09917-wOnline publication date: 17-Jul-2020
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Boidot EMarzuoli AFeron E(2016)Optimal navigation policy for an autonomous agent operating in adversarial environments2016 IEEE International Conference on Robotics and Automation (ICRA)10.1109/ICRA.2016.7487483(3154-3160)Online publication date: May-2016
https://doi.org/10.1109/ICRA.2016.7487483
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Path planning in 0/1/ weighted regions with applications

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cover image ACM Conferences

SCG '88: Proceedings of the fourth annual symposium on Computational geometry

January 1988

403 pages

ISBN:0897912705

DOI:10.1145/73393

Chairman:
H. Edelsbrunner
Univ. of Illinois, Urbana-Champaign

Copyright © 1988 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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SIGACT: ACM Special Interest Group on Algorithms and Computation Theory

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Association for Computing Machinery

New York, NY, United States

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Published: 06 January 1988

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CG88: Symposium on Computational Geometery

June 6 - 8, 1988

Illinois, Urbana-Champaign, USA

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

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Cited By

Farias RKallmann M(2020)Planar max flow maps and determination of lanes with clearanceAutonomous Robots10.1007/s10514-020-09917-wOnline publication date: 17-Jul-2020
https://doi.org/10.1007/s10514-020-09917-w
Boidot EMarzuoli AFeron E(2016)Optimal navigation policy for an autonomous agent operating in adversarial environments2016 IEEE International Conference on Robotics and Automation (ICRA)10.1109/ICRA.2016.7487483(3154-3160)Online publication date: May-2016
https://doi.org/10.1109/ICRA.2016.7487483
Elshawi RGudmundsson J(2012)Shortest Path in Transportation Network and Weighted SubdivisionsGraph Data Management10.4018/978-1-61350-053-8.ch020(463-474)Online publication date: 2012
https://doi.org/10.4018/978-1-61350-053-8.ch020
Bose PMaheshwari AShu CWuhrer S(2011)A survey of geodesic paths on 3D surfacesComputational Geometry: Theory and Applications10.1016/j.comgeo.2011.05.00644:9(486-498)Online publication date: 1-Nov-2011
https://dl.acm.org/doi/10.1016/j.comgeo.2011.05.006
Cook AWenk C(2011)Link distance and shortest path problems in the planeComputational Geometry: Theory and Applications10.1016/j.comgeo.2011.04.00444:8(442-455)Online publication date: 1-Oct-2011
https://dl.acm.org/doi/10.1016/j.comgeo.2011.04.004
Long JMould D(2009)Dendritic stylizationThe Visual Computer: International Journal of Computer Graphics10.1007/s00371-008-0217-025:3(241-253)Online publication date: 3-Feb-2009
https://dl.acm.org/doi/10.1007/s00371-008-0217-0
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
Daescu OPalmer J(2009)Modeling Optimal Beam Treatment with Weighted Regions for Bio-medical ApplicationsGeneralized Voronoi Diagram: A Geometry-Based Approach to Computational Intelligence10.1007/978-3-540-85126-4_9(215-232)Online publication date: 2009
https://doi.org/10.1007/978-3-540-85126-4_9
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
Szczerba RChen DUhran J(1998)Planning Shortest Paths among 2D and 3D Weighted Regions Using Framed-SubspacesThe International Journal of Robotics Research10.1177/02783649980170050517:5(531-546)Online publication date: 1-May-1998
https://doi.org/10.1177/027836499801700505
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