Deformable spanners and applications

Proceedings of the Annual Symposium on Computational Geometry

Volumn , Issue , 2004, Pages 190-199

  Gao, Jie ^a   Guibas, Leonidas J ^a   Nguyen, An ^a  

^a Stanford University   (United States)

Author keywords

Approximate nearest neighbor; Collision detection; Geometric k center; Kinetic data structures; Proximity maintenance; Spanner graphs; Well separated pair decomposition

Indexed keywords

ALGORITHMS; APPROXIMATION THEORY; COLLISION AVOIDANCE; COMPUTATIONAL COMPLEXITY; COMPUTATIONAL GEOMETRY; DATA STRUCTURES; POLYNOMIALS; PROBLEM SOLVING;

APPROXIMATE NEAREST NEIGHBOR; COLLISION DETECTION; GEOMETRIC Κ-CENTERS; KINETIC DATA STRUCTURES; PROXIMITY MAINTENANCE; SPANNER GRAPHS; WELL SEPARATED PAIR DECOMPOSITION;

GRAPH THEORY;

EID: 4544221005     PISSN: None     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.1145/997817.997848     Document Type: Conference Paper

References (32)

1. P. Agarwal, J. Basch, L. Guibas, J. Hershberger, and L. Zhang. Deformable free space tilings for kinetic collision detection. International Journal of Robotics Research, 21(3):179-197, 2002.
2. S. Arya, G. Das, D. M. Mount, J. S. Salowe, and M. Smid. Euclidean spanners: short, thin, and lanky. In Proc. 27th ACM Symposium on Theory Computing, pages 489-498, 1995.
3. S. Arya and T. Malamatos. Linear-size approximate voronoi diagrams. In Proc. of the 13th ACM-SIAM Symposium on Discrete Algorithms, pages 147-155, 2002.
4. S. Arya, T. Malamatos, and D. M. Mount. Space-efficient approximate voronoi diagrams. In Proc. of the 34th ACM Symposium on Theory of Computing, pages 721-730, 2002.
5. S. Arya, D. M. Mount, N. S. Netanyahu, R. Silverman, and A. Y. Wu. An optimal algorithm for approximate nearest neighbor searching fixed dimensions. J. ACM, 45(6):891-923, 1998.
6. S. Arya, D. M. Mount, and M. Smid. Randomized and deterministic algorithms for geometric spanners of small diameter. In Proc. 35th IEEE Symposium on Foundations of Computer Science, pages 703-712, 1994.
7. S. Arya and M. Smid. Efficient construction of a bounded-degree spanner with low weight. Algorithmica, 17:33-54, 1997.
8. J. Basch, L. Guibas, and J. Hershberger. Data structures for mobile data. J. Alg., 31(1):1-28, 1999.
9. Callahan and Kosaraju. Faster algorithms for some geometric graph problems in higher dimensions. In Proc. 4th ACM-SIAM Symposium on Discrete Algorithms, pages 291-300, 1993.
10. P. B. Callahan. Optimal parallel all-nearest-neighbors using the well-separated pair decomposition. In Proc. 34th IEEE Symposium on Foundations of Computer Science, pages 332-340, 1993.
11. P. B. Callahan and S. R. Kosaraju. Algorithms for dynamic closest-pair and n-body potential fields. In Proc. 6th ACM-SIAM Symposium on Discrete Algorithms, pages 263-272, 1995.
12. P. B. Callahan and S. R. Kosaraju. A decomposition of multidimensional point sets with applications to k-nearest-neighbors and n-body potential fields. J. ACM, 42:67-90, 1995.
13. M. T. Dickerson, R. L. Drysdale, and J. R. Sack. Simple algorithms for enumerating interpoint distances and finding k nearest neighbors. Internat. J. Comput. Geom. Appl., 2(3):221-239, 1992.
14. D. Eppstein. Spanning trees and spanners. In J.-R. Sack and J. Urrutia, editors, Handbook of Computational Geometry, pages 425-461. Elsevier Science Publishers B.V. North-Holland, Amsterdam, 2000.
15. J. Erickson. Dense point sets have sparse Delaunay triangulations. In Proc. 13th ACM-SIAM Sympos. Discrete Algorithms, pages 125-134, 2002.
16. T. Feder and D. H. Greene. Optimal algorithms for approximate clustering. In Proc. 20th Annu. ACM Sympos. Theory Comput., pages 434-444, 1988.
17. J. Gao, L. Guibas, J. Hershberger, L. Zhang, and A. Zhu. Discrete mobile centers. Discrete and Computational Geometry, 30(1):45-63, 2003.
18. T. Gonzalez, Clustering to minimize the maximum intercluster distance. Theoret. Comput. Sci., 38:293-306, 1985.
19. J. Gudmundsson, C. Levcopoulos, G. Narasimhan, and M. Smid. Approximate distance oracles for geometric graphs. In Proc. 13th ACM-SIAM Symposium on Discrete Algorithms, pages 828-837, 2002.
20. L. Guibas, A. Nguyen, D. Russel, and L. Zhang. Collision detection for deforming necklaces. In Proc. 18th ACM Symposium on Computational Geometry, pages 33-42, 2002.
21. L. J. Guibas. Kinetic data structures - a state of the art report. In P. K. Agarwal, L. E. Kavraki, and M. Mason, editors, Proc. Workshop Algorithmic Found. Robot., pages 191-209. A. K. Peters, Wellesley, MA, 1998.
22. J. Hershberger. Smooth kinetic maintenance of clusters. In Proc. ACM Symposium on Computational Geometry, pages 48-57, 2003.
23. P. Indyk and R. Motwani. Approximate nearest neighbors: Towards removing the curse of dimensionality. In Proc. 30th Annu. ACM Sympos. Theory Comput., pages 604-613, 1998.
24. H. P. Lenhof and M. Smid. Sequential and parallel algorithms for the k closest pairs problem. Internat. J. Comput. Geom. Appl., 5:273-288, 1995.
25. C. Levcopoulos, G. Narasimhan, and M. H. M. Smid. Improved algorithms for constructing fault-tolerant spanners. Algorithmica, 32(1):144-156, 2002.
26. M. C. Lin and J. F. Canny. A fast algorithm for incremental distance calculation. In IEEE International Conference on Robotics and Automation, pages 1008-1014, Apr. 1991.
27. I. Lotan, F. Schwarzer, D. Halperin, and J.-C. Latombe. Efficient maintenance and self-collision testing for kinematic chains. In Proc. of the 18th ACM Symposium on Computational geometry, pages 43-52, 2002.
28. G. Narasimhan and M. Smid. Approximating the stretch factor of Euclidean graphs. SIAM J. Comput., 30:978-989, 2000.
29. D. K. Pai. STRANDS: Interactive simulation of thin solids using cosserat models. In Eurographics, 2002.
30. D. Peleg. Distributed Computing: A Locality Sensitive Approach. Monographs on Discrete Mathematics and Applications. SIAM, 2000.
31. J. S. Salowe. Enumerating interdistances in space. Internat. J. Comput. Geom. Appl., 2:49-59, 1992.
32. J. M. Sullivan. Sphere packings give an explicit bound for the besicovitch covering theorem. The Journal of Geometric Analysis, 2(2):219-230, 1994.