Approximating shortest paths on a nonconvex polyhedron

SIAM Journal on Computing

Volumn 30, Issue 4, 2000, Pages 1321-1340

  Varadarajan, Kasturi R ^a   Agarwal, Pankaj K ^b  

^a University of Iowa   (United States)

^b Duke University   (United States)

Author keywords

Approximation algorithms; Computational geometry; Euclidean shortest paths

Indexed keywords

ALGORITHMS; BOUNDARY CONDITIONS; COMPUTATIONAL GEOMETRY; SET THEORY; THEOREM PROVING;

APPROXIMATION ALGORITHMS; EUCLIDEAN SHORTEST PATHS; NONCONVEX POLYHEDRON;

APPROXIMATION THEORY;

EID: 0034853038     PISSN: 00975397     EISSN: None     Source Type: Journal    
DOI: 10.1137/S0097539799352759     Document Type: Article

References (27)

1. P. K. AGARWAL, S. HAR-PELED, M. SHARIR, AND K. R. VARADARAJAN, Approximate shortest paths on a convex polytope in three dimensions, J. ACM, 44 (1997), pp. 567-584.
2. V. AKMAN, Unobstructed Shortest Paths in Polyhedral Environments, Lecture Notes in Comput. Sci. 251, Springer-Verlag, New York, 1987.
3. L. ALEKSANDROV, M. LANTHIER, A. MAHESHWARI, AND J.-R. SACK, An ε-approximation algorithm for weighted shortest paths on polyhedral surfaces, Algorithm Theory - SWAT '98, Stockholm, 1998, Lecture Notes in Comput. Sci. 1432, Springer-Verlag, Berlin, pp. 11-22.
4. L. ALEKSANDROV, A. MAHESHWARI, AND J.-R. SACK, Approximation algorithms for shortest path problems, in Proceedings of the 32nd Annual ACM Symposium on the Theory of Computing, Portland, OR, 2000, pp. 286-295.
5. S. ARYA, D. M. MOUNT, AND M. SMID, Randomized and deterministic algorithms for geometric spanners of small diameter, in Proceedings of the 35th Annual IEEE Symposium on Foundations of Computer Science, IEEE Computer Society, Los Alamitos, CA, 1994, pp. 703-712.
6. J. CHEN AND Y. HAN, Shortest paths on a polyhedron. Part I: Computing shortest paths, Internat. J. Comput. Geom. Appl., 6 (1996), pp. 127-144.
7. J. CHOI, J. SELLEN, AND C. K. YAP, Approximate Euclidean shortest paths in 3-space, Internat. J. Comput. Geom. Appl., 7 (1997), pp. 271-295.
8. K. L. CLARKSON, Approximation algorithms for shortest path motion planning, in Proceedings of the 19th Annual ACM Symposium on the Theory of Computing, New York, 1987, pp. 56-65.
9. T. H. CORMEN, C. E. LEISERSON, AND R. L. RIVEST, Introduction to Algorithms, MIT Press, Cambridge, MA, 1990.
10. X. DOUG, Finding a Geodesic Path on a 3D Triangulated Surface, Master's thesis, Mississippi State University, Starkville, MS, 1995.
11. W. R. FRANKLIN AND V. AKMAN, Shortest paths between source and goal points located on/around a convex polyhedron, in Proceedings of the 22nd Allerton Conference on Commun. Control Comput., 1984.
12. W. R. FRANKLIN AND V. AKMAN, Shortest paths in 3-space, Voronoi diagrams with barriers, and related complexity and algebraic issues, in Proceedings of the NATO Advanced Study Institute on Fundamental Algorithms for Computer Graphics, NATO Adv. Sci. Intst. Series F Comput. Systems Sci. 17, Springer-Verlag, Berlin, 1985, pp. 895-917.
13. W. R. FRANKLIN, V. AKMAN, AND C. VERRILLI, Voronoi diagrams with barriers and on polyhedra for minimal path planning, Visual Comput., 1 (1985), pp. 133-150.
14. G. N. FREDERICKSON, Fast algorithms for shortest paths in planar graphs, with applications, SIAM J. Comput., 16 (1987), pp. 1004-1022.
15. S. HAR-PELED, Constructing approximate shortest path maps in three dimensions, SIAM J. Comput., 28 (1999), pp. 1182-1197.
16. 3, Comput. Geom., 10 (1998), pp. 31-46.
17. K. KANT AND S. ZUCKER, Toward efficient trajectory planning: The path-velocity decomposition, Internat. J. Robot. Res., 5 (1986), pp. 72-89.
18. S. KAPOOR, Efficient computation of geodesic shortest paths, in Proceedings of the 31st Annual ACM Symposium on the Theory of Computing, Atlanta, GA, 1999, pp. 770-779.
19. M. LANTHIER, A. MAHESHWARI, AND J.-R. SACK, Approximating weighted shortest paths on polyhedral surfaces, in Proceedings of the 13th Annual ACM Symposium on Computational Geometry, Nice, France, 1997, pp. 274-283.
20. R. J. LIPTON AND R. E. TARJAN, A separator theorem for planar graphs, SIAM J. Appl. Math., 36 (1979), pp. 177-189.
21. C. MATA AND J. S. B. MITCHELL, A new algorithm for computing shortest paths in weighted planar subdivisions, in Proceedings of the 13th Annual ACM Symposium on Computational Geometry, Nice, France, 1997, pp. 264-273.
22. J. S. B. MITCHELL, D. M. MOUNT, AND C. H. PAPADIMITRIOU, The discrete geodesic problem, SIAM J. Comput., 16 (1987), pp. 647-668.
23. D. M. MOUNT, Voronoi Diagrams on the Surface of a Polyhedron, Technical Report 1496, Department of Computer Science, University of Maryland, College Park, MD, 1985.
24. C. H. PAPADIMITRIOU, An algorithm for shortest-path motion in three dimensions, Inform. Process. Lett., 20 (1985), pp. 259-263.
25. B. PORTER, S. MOHAMAD, AND T. CROSSLEY, Genetic computation of geodesic on three-dimensional curved surfaces, in Proceedings of the 1st International IEE/IEEE Conference on Genetic Algorithms in Engineering System: Innovations and Applications, 1995.
26. J. S. SALOWE, Constructing multidimensional spanner graphs, Internat. J. Comput. Geom. Appl., 1 (1991), pp. 99-107.
27. M. SHARIR AND A. SCHORR, On shortest paths in polyhedral spaces, SIAM J. Comput., 15 (1986), pp. 193-215.