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Approximate shortest paths and geodesic diameters on convex polytopes in three dimensions

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Published:01 August 1997Publication History
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  1. AAOS96.P.K. Agarwal, B. Aronov, J. O'Rourke, and C. Schevon. Star unfolding of a polytope with applications. SIAM J. Comput., 1996, to appear. Google ScholarGoogle ScholarDigital LibraryDigital Library
  2. AHPSV96.P.K. Agarwal, S. Har-Peled, M. Sha.dr, and K. R. Varadarajan. Approximate shortest paths on a convex polytope in three dimensions. Report CS- 1996-12, Dept. Comput. Sci., Duke Univ., Durham, NC, 1996.Google ScholarGoogle Scholar
  3. CH96.J. Chen and Y. Han. Shortest paths on a polyhedron; Part I: computing shortest paths. Int. J. Comput. Geom. # Appl., 6(2):127-144, 1996.Google ScholarGoogle Scholar
  4. Cla87.K.L. Clarkson. Approximation algorithms for shortest path motion planning. In Proc. 19th Annu. A CM Sympos. Theory Comput., pages 56-65, 1987. Google ScholarGoogle ScholarDigital LibraryDigital Library
  5. CR87.J. Canny and J. H. Reif. New lower bound techniques for robot motion planning problems. In Proc. P.8th Annu. IEEE Sympoa. Found. Camput. Sci., pages 49-60, 1987.Google ScholarGoogle ScholarDigital LibraryDigital Library
  6. CSY94.J. Choi, J. SeIlen, and C. K. Yap. Approximate Euclidean shortest path in 3-space. In Proc. l Oth Annu. A CM Sympaa. Camput. Geom., pages 41-48, 1994. Google ScholarGoogle ScholarDigital LibraryDigital Library
  7. DK85.D.P. Dobkin and D. G. Kirkpatrick. A llnear algorithm for determining the separation of convex polyhedra. J. Algorithma, 6:381-392, 1985.Google ScholarGoogle ScholarCross RefCross Ref
  8. DK90.D.P. Dobkin and D. G. Kirkpatrick. Determining the separation of preprocessed polyhedra - a unified approach. In Proc. 17th Internat. Colloq. Automata Lang. Program., volume 443 of Lecture Notes in Computer Science, pages 400-413. Springer-Verlag, 1990. Google ScholarGoogle ScholarDigital LibraryDigital Library
  9. HP97.S. Har-Peled. Constructing approximate shortest path maps in three dimensions, manuscript, 1997.Google ScholarGoogle Scholar
  10. HS95.J. Hershberger and S. Suri. Practical methods for approximating shortest paths on a convex polytope in IR3. In Proc. 6th A CM-SIAM Sympos. Discrete Algorithms, pages 447-456, 1995. Google ScholarGoogle ScholarDigital LibraryDigital Library
  11. MMP87.J.S.B. Mitchell, D. M. Mount, and C. H. Papaclimitriou. The discrete geodesic problem. SIAM J. Comput., 16:647-668, 1987. Google ScholarGoogle ScholarDigital LibraryDigital Library
  12. Pap85.C. H. Papadimitriou. An algorithm for shortest-path motion in three dimensions. Inform. Process. Lett., 20:259-263, 1985.Google ScholarGoogle ScholarCross RefCross Ref
  13. Pog73.A.V. Pogorelov. Eztrinsic Geometry of Convez Surfaces, Volume 35 of Translations of Mathematical Monographs. American Mathematical Society, Providence, Rhode Island, 1973.Google ScholarGoogle Scholar
  14. RS94.J.H. Reif and J. A. Starer. A single-exponential upper bound for finding shortest paths in three dimensions. J. A CM, 41(5):1013-1019, 1994. Google ScholarGoogle ScholarDigital LibraryDigital Library
  15. Sha87.M. Sharir. On shortest paths amidst convex polyhedra. SIAM J. Comput., 16:561-572, 1987. Google ScholarGoogle ScholarDigital LibraryDigital Library
  16. SS86.M. Sharir and A. Schorr. On shortest paths in polyhedral spaces. Siam J. Comput., 15:193- 215, 1986. Google ScholarGoogle ScholarDigital LibraryDigital Library
  17. VA96.K.R. Varadarajan and P.K. Agarwal. Approximating shortest paths on a polyhedron. manuscript, 1996.Google ScholarGoogle Scholar

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  1. Approximate shortest paths and geodesic diameters on convex polytopes in three dimensions

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        cover image ACM Conferences
        SCG '97: Proceedings of the thirteenth annual symposium on Computational geometry
        August 1997
        490 pages
        ISBN:0897918789
        DOI:10.1145/262839

        Copyright © 1997 ACM

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        Publication History

        • Published: 1 August 1997

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        SCG '97 Paper Acceptance Rate75of199submissions,38%Overall Acceptance Rate625of1,685submissions,37%

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