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Practical methods for approximating shortest paths on a convex polytope in R³

Authors:

John Hershberger,

Subhash SuriAuthors Info & Claims

SODA '95: Proceedings of the sixth annual ACM-SIAM symposium on Discrete algorithms

Pages 447 - 456

Published: 22 January 1995 Publication History

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References

[1]

P. K. Agarwal, B. Aronov, J. O'Rourke, and C. Schevon. Star unfolding of a polytope with applications. Technical Report 031, Dept. Comput. Sci., Smith College, Northampton, MA, July 1993.

Google Scholar

[2]

F. Aurenhammer. Voronoi diagrams: a survey of a fundamental geometric data structure. ACM Cornput. Surv., 23:345-405, 1991.

Digital Library

Google Scholar

[3]

C. Bajaj. The algebraic complexity of shortest paths in polyhedral spaces. In Proc. 23rd AUerton Conf. Commun. Control Comput., pages 510-517, 1985.

Google Scholar

[4]

J. Canny and J. H. Reif. New lower bound techniques for robot motion planning problems. In Proc. 28th Annu. IEEE Sympos. Found. Comput. Sci., pages 49-60, 1987.

Google Scholar

[5]

J. Chen and Y. Han. Shortest paths on a polyhedron. In Proc. 6th Annu. A CM Sympos. Comput. Geom., pages 360-369, 1990.

Digital Library

Google Scholar

[6]

J. Choi, J. Sellen, and Ch. K. Yap. Approximate Euclidean shortest path in 3-space. In Proc. l Oth Annu. A CM Sympos. Comput. Geom., 1994.

Digital Library

Google Scholar

[7]

K. L. Clarkson. Approximation algorithms for shortest path motion planning. In Proc. 19th Annu. A CM Sympos. Theory Comput., pages 56-65, 1987.

Digital Library

Google Scholar

[8]

H. EdeIsbrunner, L. J. Guibas, and J. Stolfi. Optimal point location in a monotone subdivision. SIAM J. Comput., 15:317-340, 1986.

Digital Library

Google Scholar

[9]

J. Hershberger and S. Suri. Efficient computation of Euclidean shortest paths in the plane. In Proc. 3dth Annu. IEEE Sympos. Found. Comput. Sci., pages 508-517, 1993.

Google Scholar

[10]

D. G. Kirkpatrick. Optimal search in planar subdivisions. SIAM J. Comput., 12:28-35, 1983.

Google Scholar

[11]

T. Lozano-P~rez and M. A. Wesley. An algorithm for planning collision-free paths among polyhedral obstacles. Comrnun. ACM, 22:560-570, 1979.

Digital Library

Google Scholar

[12]

J. S. B. Mitchell, D. M. Mount, and C. H. Papadimitriou. The discrete geodesic problem. SIAM J. Comput., 16:647-668, 1987.

Digital Library

Google Scholar

[13]

D. Mount. On finding shortest paths on convex polyhedra. Technical Report 1495, Department of Computer Science, University of Maryland, 1985.

Google Scholar

[14]

C. H. Papadimitriou. An algorithm for shortestpath motion in three dimensions. Inform. Process. Left., 20:259-263, 1985.

Google Scholar

[15]

F. P. Preparata and M. I. Shamos. Computational Geometry: an Introduction. Springer-Verlag, New York, NY, 1985.

Digital Library

Google Scholar

[16]

M. Sharir and A. Schorr. On shortest paths in polyhedral spaces. SIAM J. Comput., 15:193-215, 1986.

Digital Library

Google Scholar

Cited By

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Wang XFang ZWu JXin SHe Y(2017)Discrete geodesic graph (DGG) for computing geodesic distances on polyhedral surfacesComputer Aided Geometric Design10.1016/j.cagd.2017.03.01052:C(262-284)Online publication date: 1-Mar-2017
https://dl.acm.org/doi/10.1016/j.cagd.2017.03.010
Liu Y(2013)Exact geodesic metric in 2-manifold triangle meshes using edge-based data structuresComputer-Aided Design10.1016/j.cad.2012.11.00545:3(695-704)Online publication date: 1-Mar-2013
https://dl.acm.org/doi/10.1016/j.cad.2012.11.005
Xin SYing XHe Y(2011)Efficiently computing geodesic offsets on triangle meshes by the extended Xin-Wang algorithmComputer-Aided Design10.1016/j.cad.2011.08.02743:11(1468-1476)Online publication date: 1-Nov-2011
https://dl.acm.org/doi/10.1016/j.cad.2011.08.027
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Index Terms

Practical methods for approximating shortest paths on a convex polytope in R³
1. Mathematics of computing
  1. Discrete mathematics
    1. Graph theory
      1. Paths and connectivity problems
  2. Mathematical analysis
    1. Functional analysis
      1. Approximation
2. Theory of computation
  1. Design and analysis of algorithms
    1. Approximation algorithms analysis
  2. Randomness, geometry and discrete structures
    1. Computational geometry

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Published In

SODA '95: Proceedings of the sixth annual ACM-SIAM symposium on Discrete algorithms

January 1995

654 pages

ISBN:0898713498

Chairman:
Kenneth Clarkson

Publisher

Society for Industrial and Applied Mathematics

United States

Publication History

Published: 22 January 1995

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Conference

SODA95

Sponsor:

SIGACT
SIAM

SODA95: Conference on Discrete Algorithms

January 22 - 24, 1995

California, San Francisco, USA

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Overall Acceptance Rate 411 of 1,322 submissions, 31%

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Cited By

View all

Wang XFang ZWu JXin SHe Y(2017)Discrete geodesic graph (DGG) for computing geodesic distances on polyhedral surfacesComputer Aided Geometric Design10.1016/j.cagd.2017.03.01052:C(262-284)Online publication date: 1-Mar-2017
https://dl.acm.org/doi/10.1016/j.cagd.2017.03.010
Liu Y(2013)Exact geodesic metric in 2-manifold triangle meshes using edge-based data structuresComputer-Aided Design10.1016/j.cad.2012.11.00545:3(695-704)Online publication date: 1-Mar-2013
https://dl.acm.org/doi/10.1016/j.cad.2012.11.005
Xin SYing XHe Y(2011)Efficiently computing geodesic offsets on triangle meshes by the extended Xin-Wang algorithmComputer-Aided Design10.1016/j.cad.2011.08.02743:11(1468-1476)Online publication date: 1-Nov-2011
https://dl.acm.org/doi/10.1016/j.cad.2011.08.027
Xin SWang G(2009)Improving Chen and Han's algorithm on the discrete geodesic problemACM Transactions on Graphics10.1145/1559755.155976128:4(1-8)Online publication date: 8-Sep-2009
https://dl.acm.org/doi/10.1145/1559755.1559761
Xin SWang G(2007)Efficiently determining a locally exact shortest path on polyhedral surfacesComputer-Aided Design10.1016/j.cad.2007.08.00139:12(1081-1090)Online publication date: 1-Dec-2007
https://dl.acm.org/doi/10.1016/j.cad.2007.08.001
Aleksandrov LMaheshwari ASack J(2005)Determining approximate shortest paths on weighted polyhedral surfacesJournal of the ACM10.1145/1044731.104473352:1(25-53)Online publication date: 1-Jan-2005
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Lanthier MNussbaum DSack J(2003)Parallel implementation of geometric shortest path algorithmsParallel Computing10.1016/j.parco.2003.05.00429:10(1445-1479)Online publication date: 1-Oct-2003
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Har-Peled SJanardan R(1998)Constructing approximate shortest path maps in three dimensionsProceedings of the fourteenth annual symposium on Computational geometry10.1145/276884.276927(383-391)Online publication date: 7-Jun-1998
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Har-Peled SBoissonnat J(1997)Approximate shortest paths and geodesic diameters on convex polytopes in three dimensionsProceedings of the thirteenth annual symposium on Computational geometry10.1145/262839.263003(359-365)Online publication date: 1-Aug-1997
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Lanthier MMaheshwari ASack JBoissonnat J(1997)Approximating weighted shortest paths on polyhedral surfacesProceedings of the thirteenth annual symposium on Computational geometry10.1145/262839.262984(274-283)Online publication date: 1-Aug-1997
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