Nikhil Bansal
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Abstract
We give the first polylogarithmic-competitive randomized online algorithm for the k-server problem on an arbitrary finite metric space. In particular, our algorithm achieves a competitive ratio of Õ(log3 n log2 k) for any metric space on n points. Our algorithm improves upon the deterministic (2k-1)-competitive algorithm of Koutsoupias and Papadimitriou [Koutsoupias and Papadimitriou 1995] for a wide range of n.
- Dimitris Achlioptas, Marek Chrobak, and John Noga. 2000. Competitive analysis of randomized paging algorithms. Theor. Comput. Sci. 234, 1--2 (2000), 203--218. Google Scholar
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- Nikhil Bansal, Niv Buchbinder, and Joseph Naor. 2012. A primal-dual randomized algorithm for weighted paging. J. ACM 59, 4 (2012), 19. Google ScholarDigital Library
- Nikhil Bansal, Niv Buchbinder, and Joseph (Seffi) Naor. 2010a. Towards the randomized k-server conjecture: A primal-dual approach. In Proceedings of the 21st Annual ACM-SIAM Symposium on Discrete Algorithms (SODA'10). Google ScholarDigital Library
- Nikhil Bansal, Niv Buchbinder, and Joseph (Seffi) Naor. 2010b. Unfair metrical task systems on HSTs and applications. In Proceedings of the 37th International Colloquium on Automata, Languages and Programming (ICALP'10).Google Scholar
- Yair Bartal. 1996. Probabilistic approximations of metric spaces and its algorithmic applications. In Proceedings of the 37th Annual IEEE Symposium on Foundations of Computer Science (FOCS'96). 184--193. Google ScholarDigital Library
- Yair Bartal. 1998. On approximating arbitrary metrices by tree metrics. In Proceedings of the 30th Annual ACM Symposium on Theory of Computing (STOC'98). 161--168. Google ScholarDigital Library
- Yair Bartal, Avrim Blum, Carl Burch, and Andrew Tomkins. 1997. A polylog(n)-competitive algorithm for metrical task systems. In Proceedings of the 29th Annual ACM Symposium on Theory of Computing (STOC'97). 711--719. Google ScholarDigital Library
- Yair Bartal, Béla Bollobás, and Manor Mendel. 2006. Ramsey-type theorems for metric spaces with applications to online problems. J. Comput. Syst. Sci. 72, 5 (2006), 890--921. Google ScholarDigital Library
- Yair Bartal and Eddie Grove. 2000. The harmonic-server algorithm is competitive. J. ACM 47, 1 (2000), 1--15. Google ScholarDigital Library
- Yair Bartal, Nathan Linial, Manor Mendel, and Assaf Naor. 2005. On metric Ramsey-type phenomena. Ann. of Math. 162-2, 2 (2005).Google Scholar
- Avrim Blum, Carl Burch, and Adam Kalai. 1999. Finely-competitive paging. In Proceedings of the 40th Annual Symposium on Foundations of Computer Science (FOCS'99). 450. Google ScholarDigital Library
- Avrim Blum, Howard J. Karloff, Yuval Rabani, and Michael E. Saks. 2000. A decomposition theorem for task systems and bounds for randomized server problems. SIAM J. Comput. 30, 5 (2000), 1624--1661. Google ScholarDigital Library
- Allan Borodin and Ran El-Yaniv. 1998. Online Computation and Competitive Analysis. Cambridge University Press. Google ScholarDigital Library
- Marek Chrobak, Howard J. Karloff, T. H. Payne, and Sundar Vishwanathan. 1991. New results on server problems. SIAM J. Discrete Math. 4, 2 (1991), 172--181. Google ScholarDigital Library
- Marek Chrobak and Lawrence L. Larmore. 1991. An optimal on-line algorithm for k-servers on trees. SIAM J. Comput. 20, 1 (1991), 144--148. Google ScholarDigital Library
- Aaron Coté, Adam Meyerson, and Laura J. Poplawski. 2008. Randomized k-server on hierarchical binary trees. In Proceedings of the 40th Annual ACM Symposium on Theory of Computing. 227--234. Google ScholarDigital Library
- Béla Csaba and Sachin Lodha. 2006. A randomized on-line algorithm for the k-server problem on a line. Random Struct. Algorithms 29, 1 (2006), 82--104. Google ScholarDigital Library
- Jittat Fakcharoenphol, Satish Rao, and Kunal Talwar. 2003. A tight bound on approximating arbitrary metrics by tree metrics. In Proceedings of the 35th Annual ACM Symposium on Theory of Computing (STOC'03). 448--455. Google ScholarDigital Library
- Amos Fiat, Richard M. Karp, Michael Luby, Lyle A. McGeoch, Daniel Dominic Sleator, and Neal E. Young. 1991. Competitive paging algorithms. J. Algorithms 12, 4 (1991), 685--699. Google ScholarDigital Library
- Amos Fiat and Manor Mendel. 2003. Better algorithms for unfair metrical task systems and applications. SIAM J. Comput. 32, 6 (2003), 1403--1422. Google ScholarDigital Library
- A. Fiat, Y. Rabani, and Y. Ravid. 1994. Competitive k-server algorithms. J. Comput. Syst. Sci. 48, 3 (1994), 410--428. Google ScholarDigital Library
- Edward F. Grove. 1991. The harmonic online k-server algorithm is competitive. In Proceedings of the 23rd Annual ACM Symposium on Theory of Computing (STOC'91). 260--266. Google ScholarDigital Library
- Elias Koutsoupias and Christos H. Papadimitriou. 1995. On the k-server conjecture. J. ACM 42, 5 (1995), 971--983. Google ScholarDigital Library
- Mark S. Manasse, Lyle A. McGeoch, and Daniel Dominic Sleator. 1990. Competitive algorithms for server problems. J. Algorithms 11, 2 (1990), 208--230. Google ScholarDigital Library
- Lyle A. McGeoch and Daniel D. Sleator. 1991. A strongly competitive randomized paging algorithm. Algorithmica 6, 6 (1991), 816--825.Google ScholarDigital Library
- Judit Nagy-György. 2009. Randomized algorithm for the k-server problem on decomposable spaces. J. Discrete Algorithms 7, 4 (2009), 411--419. Google ScholarDigital Library
- Steven S. Seiden. 2002. A general decomposition theorem for the k-server problem. Inf. Comput. 174, 2 (2002), 193--202. Google ScholarDigital Library
- Daniel D. Sleator and Robert E. Tarjan. 1985. Amortized efficiency of list update and paging rules. Commun. ACM 28, 2 (1985), 202--208. Google ScholarDigital Library
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- A Polylogarithmic-Competitive Algorithm for the k-Server Problem
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