Approximate shortest path queries on weighted polyhedral surfaces

Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

Volumn 4162 LNCS, Issue , 2006, Pages 98-109

  Aleksandrov, Lyudmil ^a   Djidjev, Hristo N ^b   Guo, Hua ^c   Maheshwari, Anil ^c   Nussbaum, Doron ^c   Sack, Jörg Rüdiger ^c  

^a BULGARIAN ACADEMY OF SCIENCES   (Bulgaria)

^b LOS ALAMOS NATIONAL LABORATORY   (United States)

^c CARLETON UNIVERSITY   (Canada)

Author keywords

[No Author keywords available]

Indexed keywords

ALGORITHMS; APPROXIMATION THEORY; COMPUTATIONAL GEOMETRY; DATA STRUCTURES; PROBLEM SOLVING; SURFACE STRUCTURE;

APPROXIMATION PARAMETER; COMPUTE APPROXIMATE DISTANCES; GRAPH SEPARATOR ALGORITHMS; POLYHEDRAL SURFACES;

QUERY LANGUAGES;

EID: 33750060998     PISSN: 03029743     EISSN: 16113349     Source Type: Book Series    
DOI: 10.1007/11821069_9     Document Type: Conference Paper

References (15)

1. P. K. Agarwal, B. Aronov, J. O'Rourke, and C. A. Schevon. Star unfolding of a polytope with applications. SIAM J. Comput., 26(6):1689-1713, 1997.
2. P. K. Agarwal, S. Har-Peled, M. Sharir, and K.R. Varadarajan. Approximate shortest paths on a convex polytope in three dimensions. J.ACM, 44:567-584, March 1997.
3. L. Aleksandrov and H. Djidjev. Linear algorithms for partitioning embedded graphs of bounded genus. SIAM J. Disc. Math., 9(1):129-150, 1996.
4. L. Aleksandrov, H. Djidjev, H. Guo, and A. Maheshwari. Partitioning planar graphs with costs and weights. In ALENEX '02: Revised Papers from the 4th International Workshop on Algorithm Engineering and Experiments, pages 98-110, London, UK, 2002. Springer-Verlag.
5. L. Aleksandrov, M. Lanthier, A. Maheshwari, and J.-R. Sack. An ε-approximation algorithm for weighted shortest path queries on polyhedral surfaces. In Proc. 14th Euro CG Barcelona, pages 19-21, 1998.
6. L. Aleksandrov, A. Maheshwari, and J.-R. Sack. Determining approximate shortest paths on weighted polyhedral surfaces. J. ACM, 52(1):25-53, 2005.
7. B. Chazelle, D. Liu, and A. Magen. Sublinear geometric algorithms. SIAM J. Comput., 35:627-646, 2006.
8. J. Chen and Y. Han. Shortest paths on a polyhedron. In Proc. 6th ACM Symposium on Computational Geometry, pages 360-369, 1990.
9. also IJCGA 6: 127-144, 1996.
10. Y.-J. Chiang and J. S. B. Mitchell. Two-point euclidean shortest path queries in the plane. In Proc. 10th ACM-SODA, pages 215-224, Philadelphia, USA, 1999.
11. H. N. Djidjev. Linear algorithms for graph separation problems. In SWAT'88, LNCS, volume 318, pages 643-645. Springer-Verlag, Berlin, Heidelberg, 1988.
12. G. N. Frederickson. Fast algorithms for shortest paths in planar graphs. SIAM J. Comput., 16:1004-1022, 1987.
13. J. R. Gilbert, J. P. Hutchinson, and R. E. Tarjan. A separator theorem for graphs of bounded genus. J. Algorithms, 5:391-407, 1984.
14. S. Har-Peled. Approximate shortest paths and geodesic diameters on convex polytopes in three dimensions. DCG, 21:216-231, 1999.
15. S. Har-Peled. Constructing approximate shortest path maps in three dimensions. SIAM J. Comput., 28(4): 1182-1197, 1999.