Determining approximate shortest paths on weighted polyhedral surfaces

Journal of the ACM

Volumn 52, Issue 1, 2005, Pages 25-53

  Aleksandrov, L ^a   Maheshwari, A ^b   Sack, J R ^b  

^a BULGARIAN ACADEMY OF SCIENCES   (Bulgaria)

^b CARLETON UNIVERSITY   (Canada)

Author keywords

Approximation algorithms; Computational geometry; Design and analysis of algorithms; Polyhedral surfaces; Shortest path problems; Weighted paths

Indexed keywords

ALGORITHMS; COMPUTATIONAL GEOMETRY;

APPROXIMATION ALGORITHMS; POLYHEDRAL SURFACES; SHORTEST PATH PROBLEMS; WEIGHTED PATHS;

APPROXIMATION THEORY;

EID: 26844517018     PISSN: 00045411     EISSN: 00045411     Source Type: Journal    
DOI: 10.1145/1044731.1044733     Document Type: Article

References (33)

1. AGARWAL, P., HAR-PELED, S., AND KARIA, M. 2002. Computing approximate shortest paths on convex polytopes. Algorithmica 33, 227-242.
2. AGARWAL, P., HAR-PELED, S., SHARIR, M., AND VARADARAJAN, K. 1997. Approximating shortest paths on a convex polytope in three dimensions. J. ACM 44, 567-584.
3. ALEKSANDROV, L., LANTHIER, M., MAHESHWARI, A., AND SACK, J.-R. 1998. An ε-approximation algorithm for weighted shortest paths on polyhedral surfaces. In Proceedings of SWAT. Lecture Notes in Computer Science, vol. 1432, Springer-Verlag, Berlin, Germany, 11-22.
4. ALEKSANDROV, L., MAHESHWARI, A., AND SACK, J.-R. 2000. Approximation algorithms for geometric shortest path problems. In Proceedings of 32nd ACM Symposium on Theory of Computing. ACM, New York, 286-295.
5. ALEKSANDROV, L., MAHESHWARI, A., AND SACK, J.-R. 2003. An improved approximation algorithm for computing geometric shortest paths. In Proceedings of Foundations of Computation Theory. Lecture Notes in Computer Science, vol. 2751, Springer-Verlag, Berlin, Germany, 246-257.
6. ALEKSANDROV, L., MAHESHWARI, A., AND SACK, J.-R. 2004. Determining approximate shortest paths in polyhedral domains. In manuscript. Carleton University, Ottawa, Canada.
7. BAJAJ, C. 1998. The algebraic degree of geometric optimization problems. Disc. Computat. Geom. 3, 177-191.
8. CANNY, J., AND REIF, J. H. 1987. New lower bound techniques for robot motion planning problems. In Proceedings of 28th IEEE Foundation of Computer Science. (Washington, D.C.) IEEE Computer Society Press, Los Alamitos, Calif., 49-60.
9. CHAZELLE, B., Liu, D., AND MAGEN, A. 2003. Sublinear geometric algorithms. In Proceedings of 35nd ACM Symposium on Theory of Computing. ACM, New York.
10. CHEN, J., AND HAN, Y. 1996. Shortest paths on a polyhedron. Int. J. Computat. Geom. Appl. 6, 127-144.
11. HAR-PELED, S. 1999a. Approximate shortest paths and geodesic diameters on convex polytopes in three dimensions. Disc. Computat. Geom. 21, 217-231.
12. HAR-PELED, S. 1999b. Constructing approximate shortest paths maps in three dimensions. SIAM J. Comput. 28, 1182-1197.
13. HERSHBERGER, J., AND SURI, S. 1995. Practical methods for approximating shortest paths on a convex polytope. In Proceedings of 6th ACM-SIAM Symposium on Discrete Algorithms. ACM, New York, 447-456.
14. JOHANSSON, P. 1997. On a weighted distance model for injection molding. Ph.D. dissertation. Linköping Studies in Science and Technology, Linköping University, Linköping, Sweden.
15. KANAI, T., AND SUZUKI, H. 2001. Approximate shortest path on polyhedral surface and its applications. Comput. Aid. Des. 33, 11, 801-811.
16. KAPOOR, S. 1999. Efficient computation of geodesic shortest paths. In Proceedings of 31st ACM Symposium on Theory of Computing. ACM, New York, 770-779.
17. KINDL, M., SHING, M., AND ROWE, N. 1991. A stochastic approach to the weighted-region problem: Design and testing of a path annealing algorithm. In Technical Report, Computer Science. Naval Postgraduate School, Monterey, Calif.
18. LANTHIER, M., MAHESHWARI, A., AND SACK, J.-R. 2001. Approximating weighted shortest paths on polyhedral surfaces. Algorithmica 30, 4, 527-562.
19. LEE, A., DOBKIN, D., SWELDENS, W., AND SCHRODER, P. 1999. Multiresolution mesh morphing. In Computer Graphics Proceedings (SIGGRAPH 99). ACM, New York, 343-350.
20. LYUSTERNIK, L. 1964. Shortest Paths: Variational Problems (Translated and adapted from Kratchaischie linii). Mir Publishers, Moscow.
21. MINOI, J.-L. 2001. Navigation and orientation with mobile telephone. Ph.D. dissertation. Department of Computation, UMIST, UK.
22. MITCHELL, J., MOUNT, D., AND PAPADIMITRIOU, C. 1987. The discrete geodesic problem. SIAM J. Comput. 16, 647-668.
23. MITCHELL, J., AND PAPADIMITRIOU, C. 1991. The weighted region problem: Finding shortest paths through a weighted planar subdivision. J. ACM 38, 18-73.
24. MOURGUES, F., DEVERNAY, F., MALANDAIN, G., AND COSTE-MANIERE, E. 2001. 3d+t modeling of coronary artery tree from standard non simultaneous angiographic sequences. In Proceedings of the 4th International Conference on on Medical Image Computing and Computer-Assisted Intervention. Lecture Notes in Computer Science, vol. 2208, Springer-Verlag, Berlin, Germany, 1320-1322.
25. PAPADIMITRIOU, C. 1985. An algorithm for shortest path motion in three dimensions. Inf. Proc. Lett. 20, 259-263.
26. POLTHIER, K., AND SCHMIES, M. 1998. Straightest geodesies on polyhedral surfaces. In Math. Visual. Springer, Verlag, Berlin, Germany, 391.
27. REIF, J., AND SUN, Z. 2000. An efficient approximation algorithm for weighted region shortest path problem. In Proceedings of the 4th Workshop on Algorithmic Foundations of Robotics (WAFR2000). A. K. Peters Lt, Hanover, N.H., 191-203.
28. REIF, J., AND SUN, Z. 2001. Bushwack: An approximation algorithm for minimal paths through pseudo-Euclidean spaces. In Proceedings of 12th ISAAC. Lecture Notes in Computer Science, vol. 2223. Springer-Verlag, Berlin, Germany, 160-171.
29. REIF, J., AND SUN, Z. 2003. Adaptive and compact discretization for weighted region optimal path finding. In Proceedings of Foundations of Computation Theory. Lecture Notes in Computer Science, vol. 2751. Springer-Verlag, Berlin, Germany, 258-270.
30. SHARIR, M., AND SCHORR, A. 1986. On shortest paths in polyhedral spaces. SIAM J. Comput. 15, 193-215.
31. VARADARAJAN, K., AND AGARWAL, P. 2000. Approximating shortest paths on nonconvex polyhedron. SIAM J. Comput. 30, 4, 1321-1340.
32. WARNTZ, W. 1957. Transportation, social physics, and the law of refraction. Prof. Geog. 9, 4, 2-7.
33. ZIEGELMANN, M. 2001. Constrained shortest paths and related problems. Ph.D. dissertation. Max-Planck Institut fur Informatik (submitted at Universität des Saarlandes), Saarbrücken, Germany.