Efficient distributed approximation algorithms via probabilistic tree embeddings

Distributed Computing

Volumn 25, Issue 3, 2012, Pages 189-205

  Khan, Maleq ^a   Kuhn, Fabian ^b   Malkhi, Dahlia ^c   Pandurangan, Gopal ^d   Talwar, Kunal ^c  

^a VIRGINIA BIOINFORMATICS INSTITUTE   (United States)

^b UNIVERSITY OF LUGANO   (Switzerland)

^c MICROSOFT RESEARCH   (United States)

^d NANYANG TECHNOLOGICAL UNIVERSITY   (Singapore)

Author keywords

Generalized steiner forests; Leader election; Least element lists; Metric spaces; Optimum routing cost spanning trees; Probabilistic tree embeddings; Shortest paths

Indexed keywords

COST SPANNING; EMBEDDINGS; LEADER ELECTION; LEAST ELEMENT LISTS; METRIC SPACES; SHORTEST PATH; STEINER FORESTS;

APPROXIMATION ALGORITHMS; DATA STRUCTURES; FORESTRY; OPTIMIZATION;

GRAPH THEORY;

ALGORITHMS; DATA; FORESTRY; FORESTS; OPTIMIZATION; STRUCTURES; TREES;

EID: 84863419889     PISSN: 01782770     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00446-012-0157-9     Document Type: Article

References (35)

1. Y. Afek M. Ricklin 1993 Sparser: a paradigm for running distributed algorithms J. Algorithms 14 2 316 328 1201931 0773.68034 10.1006/jagm.1993.1016
2. Awerbuch, B.: Optimal distributed algorithms for minimum weight spanning tree, counting, leader election, and related problems. In: Proceedings of the 19th ACM Symposium on Theory of Computing (STOC), pp. 230-240. ACM (1987) (Pubitemid 18643410)
3. Bartal, Y.: Probabilistic approximations of metric spaces and its algorithmic applications. In: Proceedings of the 37th Annual Symposium on Foundations of Computer Science (FOCS), pp. 184-193. IEEE Computer Society (1996)
4. Bartal, Y.: On approximating arbitrary metrics by tree metrics. In: Proceedings of the 30th ACM Symposium on Theory of Computing (STOC), pp. 161-168. ACM (1998)
5. Bartal, Y.; Byers, J.; Raz, D.: Global optimization using local information with applications to flow control. In: Proceedings of the 38th Annual Symposium on Foundations of Computer Science (FOCS), pp. 303-312. IEEE Computer Society (1997)
6. Chalermsook, P.; Fakcharoenphol, J.: Simple distributed algorithms for approximating minimum Steiner trees. In: Proceedings of the 11th Annual International Conference on Computing and Combinatorics (COCOON), pp. 380-389. Springer (2005) (Pubitemid 41450216)
7. Charikar, M.; Chekuri, C.; Goel, A.; Guha, S.; Plotkin, S.: Approximating a finite metric by a small number of tree metrics. In: Proceedings of the 39th Annual Symposium on Foundations of Computer Science (FOCS), pp. 379-388. IEEE Computer Society (1998)
8. E. Cohen 1997 Size-estimation framework with applications to transitive closure and reachability J. Comput. Syst. Sci. 55 3 441 453 0897.68075 10.1006/jcss.1997.1534 (Pubitemid 127432363)
9. E. Cohen H. Kaplan 2007 Spatially-decaying aggregation over a network J. Comput. Syst. Sci. 73 3 265 288 2310524 1115.68016 10.1016/j.jcss.2006.10.016 (Pubitemid 46027074)
10. Sarma, A.; Holzer, S.; Kor, L.; Korman, A.; Nanongkai, D.; Pandurangan, G.; Peleg, D.; Wattenhofer, R.: Distributed verification and hardness of distributed approximation. In: Proceedings of the 43rd ACM Symposium on Theory of Computing (STOC), pp. 363-372. ACM (2011)
11. Dubhashi, D.; Grandioni, F.; Panconesi, A.: Distributed approximation algorithms via LP duality and randomization. In: Gonzalez T. (ed.) Handbook of Approximation Algorithms and Metaheuristics, CRC Press, Boca Raton (2007)
12. M. Elkin 2005 Computing almost shortest paths ACM Trans. Algorithms 1 2 283 322 2190125 10.1145/1103963.1103968
13. M. Elkin 2004 Distributed approximation: a survey ACM SIGACT News 35 4 40 57 10.1145/1054916.1054931
14. M. Elkin 2006 A faster distributed protocol for constructing a minimum spanning tree J. Comput. Syst. Sci. 72 8 1282 1308 2273409 1118.68026 10.1016/j.jcss.2006.07.002 (Pubitemid 44647248)
15. M. Elkin 2006 An unconditional lower bound on the time-approximation tradeoff for the minimum spanning tree problem SIAM J. Comput. 36 2 433 456 2247735 1116.05077 10.1137/S0097539704441058 (Pubitemid 46627295)
16. J. Fakcharoenphol S. Rao K. Talwar 2004 A tight bound on approximating arbitrary metrics by tree metrics J. Comput. Syst. Sci. 69 3 485 497 2087946 1071.68082 10.1016/j.jcss.2004.04.011
17. R. Gallager P. Humblet P. Spira 1983 A distributed algorithm for minimum-weight spanning trees ACM Trans. Program. Lang. Syst. 5 1 66 77 0498.68040 10.1145/357195.357200
18. Grandoni, F.; Könemann, J.; Panconesi, A.; Sozio, M.: Primal-dual based distributed algorithms for vertex cover with semi-hard capacities. In: Proceedings of the 24th ACM symposium on Principles of distributed computing (PODC), pp. 118-125. ACM (2005) (Pubitemid 43218379)
19. L. Jia R. Rajaraman R. Suel 2002 An efficient distributed algorithm for constructing small dominating sets Distrib. Comput. 15 4 193 205 10.1007/s00446-002-0078-0
20. M. Khan G. Pandurangan 2008 A fast distributed approximation algorithm for minimum spanning trees Distrib. Comput. 20 391 402 10.1007/s00446-007-0047-8 (Pubitemid 351464295)
21. Kuhn, F.; Moscibroda, T.; Wattenhofer, R.: What cannot be computed locally! In: Proceedings of the 23rd ACM symposium on Principles of distributed computing (PODC), pp. 300-309. ACM (2004)
22. Kuhn, F.; Moscibroda, T.; Wattenhofer, R.: The price of being near-sighted. In: Proceedings of the 17th ACM-SIAM Symposium on Discrete Algorithms (SODA). pp. 980-989. SIAM (2006) (Pubitemid 43275324)
23. S. Kutten D. Peleg 1998 Fast distributed construction of k-dominating sets and applications J. Algorithms 28 40 66 1627021 0919.68052 10.1006/jagm.1998.0929 (Pubitemid 128638748)
24. Nutov, Z.; Sadeh, A.: Distributed primal-dual approximation algorithms for network design problems. Manuscript, (2009). http://www.openu.ac.il/home/ nutov/distributed.pdf
25. A. Panconesi A. Srinivasan 1997 Randomized distributed edge coloring via an extension of the Chernoff-Hoeffding bounds SIAM J. Comput. 26 350 368 1438520 0867.05063 10.1137/S0097539793250767 (Pubitemid 127652069)
26. Pandurangan G.; Khan M.: Theory of communication networks. In: Atallah, M.J.; Blanton, M. (eds) Algorithms and Theory of Computation Handbook.; CRC Press, Boca Raton (2009)
27. Papadimitriou, C.; Yannakakis, M.: Linear programming without matrix. In: Proceedings of the 25th ACM Symposium on Theory of Computing (STOC), pp. 121-129, ACM (1993)
28. D. Peleg 1990 A time optimal leader election algorithm in general networks J. Parallel Distrib. Comput. 8 96 99 10.1016/0743-7315(90)90074-Y (Pubitemid 20646646)
29. Peleg D.: Distributed Computing: A Locality-Sensitive Approach. SIAM, (2000)
30. Peleg, D.; Rabinovich, V.: A near-tight lower bound on the time complexity of distributed mst construction. In: Proceedings of the 40th Annual Symposium on Foundations of Computer Science (FOCS), pp. 379-388. IEEE Computer Society (1999)
31. Tel G.: Introduction to Distributed Algorithms. Cambridge University Press, Cambridge (1994)
32. Vazirani V.: Approximation Algorithms. Springer, New York (2004)
33. Wattenhofer, M.; Wattenhofer, R.: Distributed weighted matching. In: Proceedings of the 18th Conference on Distributed Computing (DISC), pp. 335-348. Springer, New York (2004) (Pubitemid 39750524)
34. Wu B.; Chao K.: Spanning Trees and Optimization Problems. Chapman and Hall/CRC, Boca Raton (2004)
35. Wu, B.; Lancia, G.; Bafna, V.; Chao, K.; Ravi, R.; Tang, C.: A polynomial time approximation scheme for minimum routing cost spanning trees. In: Proceedings of the 9th ACM-SIAM Symposium on Discrete Algorithms (SODA). pp. 21-32. SIAM (1998)