Fault-tolerant geometric spanners

Discrete and Computational Geometry

Volumn 32, Issue 2, 2004, Pages 207-230

  Czumaj, Artur ^a   Zhao, Hairong ^a  

^a University Heights   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 4344616177     PISSN: 01795376     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00454-004-1121-7     Document Type: Conference Paper

References (37)

1. I. Althöfer, G. Das, D. Dobkin, D. Joseph, and J. Scares. On sparse spanners of weighted graphs. Discrete & Computational Geometry, 9:81-100, 1993. A preliminary version entitled "Generating sparse spanners for weighted graphs" appeared in J. R. Gilbert and R. G. Karlsson, editors, Proceedings of the 2nd Scandinavian Workshop on Algorithm Theory, Bergen, Norway, July 11-14, 1990, pages 26-37. Volume 447 of Lecture Notes in Computer Science. Springer-Verlag, Berlin.
2. I. Althöfer, G. Das, D. Dobkin, D. Joseph, and J. Scares. On sparse spanners of weighted graphs. Discrete & Computational Geometry, 9:81-100, 1993. A preliminary version entitled "Generating sparse spanners for weighted graphs" appeared in J. R. Gilbert and R. G. Karlsson, editors, Proceedings of the 2nd Scandinavian Workshop on Algorithm Theory, Bergen, Norway, July 11-14, 1990, pages 26-37. Volume 447 of Lecture Notes in Computer Science. Springer-Verlag, Berlin.
3. S. Arya, G. Das, D. M. Mount, J. S. Salowe, and M. Smid. Euclidean spanners: Short, thin, and lanky. In Proceedings of the 11th Annual ACM Symposium on Theory of Computing, Las Vegas, NV, May 29 - June 1, 1995, pages 489-498. ACM Press, New York.
4. S. Arya and M. Smid. Efficient construction of a bounded-degree spanner with low weight. Algorithmica, 17(l):33-54, January 1997. A preliminary version appeared in J. van Leeuwen, editor, Proceedings of the 2nd Annual European Symposium on Algorithms, Utrecht, The Netherlands, September 26-28, 1994, pages 48-59. Volume 855 of Lecture Notes in Computer Science. Springer-Verlag, Berlin.
5. S. Arya and M. Smid. Efficient construction of a bounded-degree spanner with low weight. Algorithmica, 17(l):33-54, January 1997. A preliminary version appeared in J. van Leeuwen, editor, Proceedings of the 2nd Annual European Symposium on Algorithms, Utrecht, The Netherlands, September 26-28, 1994, pages 48-59. Volume 855 of Lecture Notes in Computer Science. Springer-Verlag, Berlin.
6. M. de Barg, M. van Kreveld, M. Overmars, and Computational Geometry - Algorithms and Applications. Springer-Verlag, Berlin, 1997.
7. M. Bollobas. Modern Graph Theory. Springer-Verlag, Berlin, 1998.
8. P. B. Callahan and S. R. Kosaraju. A decomposition of multidimensional point sets with applications to k-nearest-neighbors and n-body potential fields. Journal of the ACM, 42(1):67-90, January 1995. A preliminary version appeared in Proceedings of the 24th Annual ACM Symposium on Theory of Computing, Victoria, British Columbia, Canada, May 4-6, 1992, pages 546-556. ACM Press, New York.
9. P. B. Callahan and S. R. Kosaraju. A decomposition of multidimensional point sets with applications to k-nearest-neighbors and n-body potential fields. Journal of the ACM, 42(1):67-90, January 1995. A preliminary version appeared in Proceedings of the 24th Annual ACM Symposium on Theory of Computing, Victoria, British Columbia, Canada, May 4-6, 1992, pages 546-556. ACM Press, New York.
10. B. Chandra, G. Das, G. Narasimhan, and J. Soares. New sparseness results on graph spanners. In Proceedings of the 8th Annual ACM Symposium on Computational Geometry, Berlin, Germany, June 10-12,1992, pages 192-201. ACM Press, New York.
11. P. L. Chew. There is a planar graph as good as the complete graph. In Proceedings of the 2nd Annual ACM Symposium on Computational Geometry, Yorktown Heights, NY, June 2-4, 1986, pages 169-177. ACM Press, New York.
12. A. Czumaj and A. Lingas. On approximability of the minimum-cost k-connected spanning subgraph problem. In Proceedings of the 10th Annual ACM-SIAM Symposium on Discrete Algorithms, Baltimore, MD, January 17-19, 1999, pages 281-290. SIAM, Philadelphia, PA.
13. A. Czumaj and A. Lingas. Fast approximation schemes for Euclidean multi-connectivity problems. In U. Montanari, J. D. P. Rolim, and E. Welzl, editors, Proceedings of the 21th Annual International Colloquium on Automata, Languages and Programming, Geneva, Switzerland, July 9-15, 2000, pages 856-868. Volume 1853 of Lecture Notes in Computer Science. Springer-Verlag, Berlin.
14. A. Czumaj, A. Lingas. and H. Zhao. Polynomial-time approximation schemes for the Euclidean survivable network design problem. In P. Widmayer, F. Triguero, R. Morales, M. Hennessy, S. Eidenbenz, and R. Conejo, editors, Proceedings of the 29th Annual International Colloquium on Automata, Languages and Programming, Malaga, Spain, July 8-13, 2002, pages 973-984. Volume 2380 of Lecture Notes in Computer Science. Springer-Verlag, Berlin.
15. G. Das, P. Heffernan, and G. Narasimhan. Optimally sparse spanners in 3-dimensional Euclidean space. In Proceedings of the 9th Annual ACM Symposium on Computational Geometry, San Diego, CA, May 19-21, 1993, pages 53-62. ACM Press, New York.
16. G. Das and G. Narasimhan. A fast algorithm for constructing sparse Euclidean spanners. International Journal of Computational Geometry and Applications, 7(4):293-315, 1997. A preliminary version appeared in Proceedings of the 10th Annual ACM Symposium on Computational Geometry, Stony Brook, NY, June 6-8, 1994, pages 132-139. ACM Press, New York.
17. G. Das and G. Narasimhan. A fast algorithm for constructing sparse Euclidean spanners. International Journal of Computational Geometry and Applications, 7(4):293-315, 1997. A preliminary version appeared in Proceedings of the 10th Annual ACM Symposium on Computational Geometry, Stony Brook, NY, June 6-8, 1994, pages 132-139. ACM Press, New York.
18. G. Das, G. Narasimhan, and J. Salowe. A new way to weigh malnourished Euclidean graphs. In Proceedings of the 6th Annual ACM-SIAM Symposium on Discrete Algorithms, San Francisco, CA, January 22-24, 1995, pages 215-222. SIAM, Philadelphia, PA.
19. D. Eppstein. Spanning trees and spanners. In J.-R. Sack and J. Urrutia, editors, Handbook of Computational Geometry, chapter 9, pages 425-461. Elsevier Science, Amsterdam, 1997.
20. J. Gao, L. J. Guibas, J. Hershburger, L. Zhang, and A. Zhu. Geometric spanner for routing in mobile networks. In Proceedings of the 2nd ACM Symposium on Mobile Ad Hoc Networking & Computing (MobiHoc 2001), Long Beach, CA, October 4-5, 2001, pages 45-55.
21. M. Grünewald, T. Lukovszki, C. Schindelhauer, and K. Volbert. Distributed maintenance of resource efficient wireless network topologies. In B. Monien and R. Feldmann, editors, Proceedings of the 8th Euro-Par, Paderborn, Germany, August 27-30, 2002, pages 935-946. Volume 2400 of Lecture Notes in Computer Science. Springer-Verlag, Berlin.
22. J. Gudmundsson, C. Levcopoulos, and G. Narasimhan. Fast greedy algorithms for constructing sparse geometric spanners. SIAM Journal on Computing, 31(5):1479-1500, August 2002. A preliminary version appeared in M. M. Halldórsson, editor, Proceedings of the 1th Scandinavian Workshop on Algorithm Theory, Bergen, Norway, July 5-7, 2000, pages 314-327. Volume 1851 of Lecture Notes in Computer Science. Springer-Verlag, Berlin.
23. J. Gudmundsson, C. Levcopoulos, and G. Narasimhan. Fast greedy algorithms for constructing sparse geometric spanners. SIAM Journal on Computing, 31(5):1479-1500, August 2002. A preliminary version appeared in M. M. Halldórsson, editor, Proceedings of the 1th Scandinavian Workshop on Algorithm Theory, Bergen, Norway, July 5-7, 2000, pages 314-327. Volume 1851 of Lecture Notes in Computer Science. Springer-Verlag, Berlin.
24. C. Levcopoulos and A. Lingas. There are planar graphs almost as good as the complete graphs and almost as cheap as minimum spanning trees. Algorithmica, 8:251-256, 1992. A preliminary version appeared in H. Djidjev, editor, Proceedings of the International Symposium on Optimal Algorithms, Varna, Bulgaria, 1989, pages 9-13. Volume 401 of Lecture Notes in Computer Science. Springer-Verlag, Berlin.
25. C. Levcopoulos and A. Lingas. There are planar graphs almost as good as the complete graphs and almost as cheap as minimum spanning trees. Algorithmica, 8:251-256, 1992. A preliminary version appeared in H. Djidjev, editor, Proceedings of the International Symposium on Optimal Algorithms, Varna, Bulgaria, 1989, pages 9-13. Volume 401 of Lecture Notes in Computer Science. Springer-Verlag, Berlin.
26. C. Levcopoulos, G. Narasimhan, and M. H. M. Smid. Improved algorithms for constructing fault-tolerant spanners. Algorithmica, 32(1): 144-156, 2002. A preliminary version appeared in Proceedings of the 30th Annual ACM Symposium on Theory of Computing, Dallas, TX, May 23-26, 1998, pages 186-195, ACM Press, New York.
27. C. Levcopoulos, G. Narasimhan, and M. H. M. Smid. Improved algorithms for constructing fault-tolerant spanners. Algorithmica, 32(1): 144-156, 2002. A preliminary version appeared in Proceedings of the 30th Annual ACM Symposium on Theory of Computing, Dallas, TX, May 23-26, 1998, pages 186-195, ACM Press, New York.
28. T. Lukovszki. New results on fault tolerant geometric spanners. In F. Dehne, A. Gupta, J.-R. Sack, and R. Tamassia, editors, Proceedings of the 6th Workshop on Algorithms and Data Structures, Vancouver, Canada, August 11-14, 1999, pages 193-204. Volume 1663 of Lecture Notes in Computer Science. Springer-Verlag, Berlin.
29. T. Lukovszki. New Results on Geometric Spanners and Their Applications. Ph.D. thesis, University of Paderborn, 1999.
30. K. Mehlhorn and S. Näher. Dynamic fractional cascading. Algorithmica, 5:215-241, 1990.
31. D. Peleg. Distributed Computing: A Locality-Sensitive Approach. Society for Industrial and Applied Mathematics, Philadelphia, PA, 2000.
32. D. Peleg and A. Schäffer. Graph spanners. Journal of Graph Theory, 13:99-116, 1989.
33. R. Rajaraman. Topology control and routing in ad hoc networks: a survey. SIGACT News, 33:60-73, June 2002.
34. S. B. Rao and W. D. Smith. Approximating geometrical graphs via "spanners" and "banyans". In Proceedings of the 30th Annual ACM Symposium on Theory of Computing, Dallas, TX, May 23-26, 1998, pages 540-550. ACM Press, New York.
35. J. Ruppert and R. Seidel. Approximating the d-dimensional complete Euclidean graph. In Proceedings of the 3rd Canadian Conference on Computational Geometry, Simon Fraser University, Vancouver, Canada, August 6-10, 1991, pages 207-210.
36. M. Smid. Closest-point problems in computational geometry. In J.-R. Sack and J. Urrutia, editors, Handbook of Computational Geometry, chapter 20, pages 877-935. Elsevier Science Amsterdam, 1997.
37. A. C. Yao. On constructing minimum spanning trees in k-dimensional spaces and related problems. SIAM Journal on Computing, 11:721-736, 1982.