Distributed algorithms for ultrasparse spanners and linear size skeletons

Distributed Computing

Volumn 22, Issue 3, 2010, Pages 147-166

  Pettie, Seth ^a  

^a UNIVERSITY OF MICHIGAN   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

ADDITIVE DISTORTION; ADDITIVE SPANNERS; DISTRIBUTED ALGORITHM; DISTRIBUTED NETWORKS; EFFICIENT ALGORITHM; GOLDEN RATIO; LOW DISTORTION; LOWER BOUNDS; NON-TRIVIAL; SHORT MESSAGE; SUBLINEAR; TIME STEP;

COMPUTATION THEORY; OPTICAL DEVICES;

ALGORITHMS;

EID: 77649271655     PISSN: 01782770     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00446-009-0091-7     Document Type: Article

References (41)

1. Abraham, I., Gavoille, C., Malkhi, D.: On space-stretch trade-offs: upper bounds. In: Proceedings of the 18th Annual ACM Symposium on Parallel Algorithms and Architectures (SPAA), pp. 217-224 (2006)
2. Abraham, I., Gavoille, C., Malkhi, D., Nisan, N., Thorup, M.: Compact name-independent routing with minimum stretch. In: Proceedings of the 16th Annual ACM Symposium on Parallel Algorithms and Architectures (SPAA) pp. 20-24 (2004)
3. D. Aingworth C. Chekuri P. Indyk R. Motwani 1999 Fast estimation of diameter and shortest paths (without matrix multiplication) SIAM J. Comput. 28 4 1167 1181 0926.68093 10.1137/S0097539796303421 1681058
4. I. Althöfer G. Das D. Dobkin D. Joseph J. Soares 1993 On sparse spanners of weighted graphs Discrete Comput. Geom. 9 81 100 0762.05039 10.1007/BF02189308 1184695
5. S. Baswana 2008 Streaming algorithm for graph spanners-single pass and constant processing time per edge Inf. Proc. Lett. 106 3 110 114 10.1016/j.ipl.2007.11.001 2399880
6. Baswana, S., Kavitha, T.: Faster algorithms for approximate distance oracles and all-pairs small stretch paths. In: Proceedings of the 47th IEEE Symposium on Foundations of Computer Science (FOCS), pp. 591-602. (2006)
7. Baswana, S., Kavitha, T., Mehlhorn, K., Pettie, S.: Additive spanners and (α, β)-spanners. ACM Trans. on Algorithms (2009)
8. Baswana, S., Sarkar, S.: Fully dynamic algorithms for graph spanners with poly-logaritmic update time. In: Proceedings of the 19th ACM-SIAM Symposium on Discrete Algorithms (SODA), pp. 1125-1134 (2008)
9. 2 log n) time ACM Trans. Algorithms 2 4 557 577 10.1145/1198513.1198518 2284245 (Pubitemid 46174061)
10. S. Baswana S. Sen 2007 A simple and linear time randomized algorithm for computing sparse spanners in weighted graphs J. Random Struct. Algs. 30 4 532 563 1118.68582 10.1002/rsa.20130 2326157
11. L.J. Cowen 2001 Compact routing with minimum stretch J. Algor. 28 170 183 10.1006/jagm.2000.1134 1810436 (Pubitemid 33667205)
12. L.J. Cowen C.G. Wagner 2004 Compact roundtrip routing in directed networks J. Algor. 50 1 79 95 1090.68115 10.1016/j.jalgor.2003.08.001 2028584
13. B. Derbel C. Gavoille 2008 Fast deterministic distributed algorithms for sparse spanners Theor. Comput. Sci. 399 1-2 83 100 1165.68065 10.1016/j.tcs.2008.02.019 2416952
14. Derbel, B., Gavoille, C., Peleg D.: Deterministic distributed construction of linear stretch spanners in polylogarithmic time. In: Proceedings of the 21st International Symposium on Distributed Computing (DISC) pp. 179-192. (2007)
15. Derbel, B., Gavoille, C., Peleg, D., Viennot, L.: On the locality of distributed sparse spanner construction. In: Proceedings 27th Annual ACM Symposium on Principles of Distributed Computing (PODC), pp. 273-282. (2008)
16. Derbel, B., Gavoille, C., Peleg, D., Viennot, L.: Local computation of nearly additive spanners. In: Proceedings 23rd International Symposium on Distributed Computing (DISC), LNCS volume 5805, pp. 176-190. (2009)
17. D. Dor S. Halperin U. Zwick 2000 All-pairs almost shortest paths SIAM J. Comput. 29 5 1740 1759 0948.05047 10.1137/S0097539797327908 1744845 (Pubitemid 32021664)
18. D. Dubhashi A. Mei A. Panconesi J. Radhakrishnan A. Srinivasan 2005 Fast distributed algorithms for (weakly) connected dominating sets and linear-size skeletons J. Comput. Syst. Sci. 71 4 467 479 1085.68184 10.1016/j.jcss.2005.04. 002 2178075 (Pubitemid 41526425)
19. M. Elkin 2005 Computing almost shortest paths ACM Trans. Algorithms 1 2 283 323 10.1145/1103963.1103968 2190125
20. Elkin, M.: A near-optimal distributed fully dynamic algorithm for maintaining sparse spanners. In: Proceedings of the 26th International Symposium on Principles of Distributed Computing (PODC), pp. 185-194 (2007)
21. Elkin, M.: Streaming and fully dynamic centralized algorithms for maintaining sparse spanners. In: Proceedings of the 34th International Colloquium on Automata, Languages, and Programming (ICALP), pp. 716-727 (2007)
22. Elkin, M., Peleg, D.: (1+ε β)-spanner constructions for general graphs. In: Proceedings of the 33rd Annual ACM Symposium on Theory of Computing (STOC), pp. 173-182 (2001)
23. M. Elkin D. Peleg 2004 (1+ε β)-spanner constructions for general graphs SIAM J. Comput. 33 3 608 631 1056.05134 10.1137/S0097539701393384 2066645
24. M. Elkin J. Zhang 2006 Efficient algorithms for constructing (1+ε β)-spanners in the distributed and streaming models Distrib. Comput. 18 5 375 385 10.1007/s00446-005-0147-2
25. Erdos, P.: Extremal problems in graph theory. In Theory of Graphs and its Applications (Proceedings of Symposium Smolenice, 1963), pp. 29-36. Publ. House Czechoslovak Acad. Sci., Prague (1963)
26. C. Gavoille D. Peleg S. Pérennes R. Raz 2004 Distance labeling in graphs J. Algor. 53 85 112 1068.68104 10.1016/j.jalgor.2004.05.002
27. M. Mendel A. Naor 2007 Ramsey partitions and proximity data structures J. Eur. Math. Soc 9 2 253 275 1122.68043 10.4171/JEMS/79 2293956
28. Narasimhan G., Smid M.: Geometric Spanner Networks. Cambridge University Press, Cambridge, England (2007)
29. Panconesi, A.: Personal communication (2008)
30. Peleg, D.: Distributed computing: A locality-sensitive approach. SIAM (2000)
31. D. Peleg E. Upfal 1989 A trade-off between space amd efficiency for routing tables J. ACM 36 3 510 530 0900.68262 10.1145/65950.65953 1072235
32. Pettie, S.: Low distortion spanners. ACM Trans. on Algorithms (to appear)
33. Pettie, S.: Low distortion spanners. In: Proceedings of the 34th International Colloquium on Automata, Languages, and Programming (ICALP), pp. 78-89 (2007)
34. Roditty, L., Thorup, M., Zwick, U.: Roundtrip spanners and roundtrip routing in directed graphs. In: Proceedings of the 13th ACM-SIAM Symposium On Discrete Algorithms (SODA), pp. 844-851 (2002)
35. Roditty, L., Thorup, M., Zwick, U.: Deterministic constructions of approximate distance oracles and spanners. In: Proceedings of the 32nd International Colloquium on Automata, Languages, and Programming (ICALP), pp. 261-272 (2005)
36. Roditty, L., Zwick, U.: On dynamic shortest paths problems. In: Proceedings of the 12th Annual European Symposium on Algorithms (ESA), pp. 580-591 (2004)
37. Thorup, M. Zwick, U.: Compact routing schemes. In: Proceedings of the 13th ACM Symposium on Parallel Algorithms and Architectures (SPAA), pp. 1-10 (2001)
38. M. Thorup U. Zwick 2005 Approximate distance oracles J. ACM 52 1 1 24 1175.68303 10.1145/1044731.1044732 2143683 (Pubitemid 43078379)
39. Thorup, M., Zwick, U.: Spanners and emulators with sublinear distance errors. In: Proceedings of the 17th ACM-SIAM Symposium on Discrete Algorithms (SODA), pp. 802-809 (2006)
40. 10s J. Comb. Theory Ser. B 52 1 113 116 0755.05060 10.1016/0095-8956(91)90097-4 1109426
41. Woodruff, D.: Lower bounds for additive spanners, emulators, and more. In: Proceedings of the 47th Annual IEEE Symposium on Foundations of Computer Science (FOCS), pp. 389-398 (2006)