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Memoryless Algorithms for the Generalized k-server Problem on Uniform Metrics [article]

Dimitris Christou, Dimitris Fotakis, Grigorios Koumoutsos
2020 arXiv   pre-print
We consider the generalized k-server problem on uniform metrics. We study the power of memoryless algorithms and show tight bounds of Θ(k!) on their competitive ratio.  ...  This improves the ≈ 2^2^k doubly-exponential bound of Chiplunkar and Vishwanathan for the more general setting of uniform metrics with different weights.  ...  Memoryless Algorithms for Generalized k-server: Recently Chiplunkar and Vishnawathan [11] studied randomized memoryless algorithms in weighted uniform metrics.  ... 
arXiv:2007.08669v1 fatcat:zbgfp6xdvjg6zlckwbau6eybfq

On Randomized Memoryless Algorithms for the Weighted K-Server Problem

Ashish Chiplunkar, Sundar Vishwanathan
2013 2013 IEEE 54th Annual Symposium on Foundations of Computer Science  
The weighted k-server problem is a generalization of the k-server problem in which the cost of moving a server of weight β_i through a distance d is β_i· d.  ...  The above result has two important implications. Firstly this yields an α_k-competitive memoryless algorithm for the weighted k-server problem on uniform spaces.  ...  Acknowledgment The authors would like to thank Nikhil Bansal for pointing them to some important work on the weighted k-server problem.  ... 
doi:10.1109/focs.2013.10 dblp:conf/focs/ChiplunkarV13 fatcat:e67mc5h7ljh6lnhzh4a6em4hmy

A lower bound on the competitivity of memoryless algorithms for a generalization of the CNN problem

Yves F. Verhoeven
2006 Theoretical Computer Science  
This generalizes in several aspects the lower bounds obtained by Koutsoupias and Taylor [The CNN Problem and other k-server variants, Theoret. Comput.  ...  Sci. 324 (2004) 347-359] for the original problem. The proof consists in the analysis of carefully selected random walks, which appear naturally in the framework of memoryless algorithms.  ...  Acknowledgments The author would like to thank Miklos Santha for bringing to his attention this problem and for all his advice.  ... 
doi:10.1016/j.tcs.2006.01.047 fatcat:mpkecyfgcvgldih63qjzkoplme

The -server problem

Elias Koutsoupias
2009 Computer Science Review  
The k-server conjecture, which was posed more that two decades ago when the problem was first studied within the competitive analysis framework, is still open and has been a major driving force for the  ...  Supported in part by IST-2008-215270 (FRONTS). 1 Although for deterministic algorithms the configurations can be inferred from C0 and the sequence of requests r, randomized algorithms are based on all  ...  For the weighted paging problem (equivalent to the k-server problem on stars where the requests are at the end of leaves), Irani [Ira97] established the randomized k-server conjecture for the weighted  ... 
doi:10.1016/j.cosrev.2009.04.002 fatcat:rrschyzb3zdd7gj6h5cmvjc534

The weighted 2-server problem

Marek Chrobak, Jiřı́ Sgall
2004 Theoretical Computer Science  
For arbitrary metric spaces, in contrast with the non-weighted case, we prove that there is no memoryless randomized algorithm with ÿnite competitive ratio.  ...  We consider a generalization of the 2-server problem in which servers have di erent costs.  ...  Acknowledgements We would like to thank the anonymous referees for pointing out some mistakes and for insightful comments that helped us improve the presentation.  ... 
doi:10.1016/j.tcs.2004.05.020 fatcat:7f6l73ue6nawzfufwaxybsjt2e

An Optimal On-Line Algorithm for K Servers on Trees

Marek Chrobak, Lawrence L. Larmore
1991 SIAM journal on computing (Print)  
We investigate the k-server problem when the metric space is a tree. For this case we present an on-line k-competitive algorithm for k servers. The competitiveness ratio k is optimal.  ...  The algorithm is memoryless, in the sense that it does not use any information from the past.  ...  Allan Borodin pointed out to us that our potential function can be espressed by the formula we currently use in the paper. The same formula was used in 3].  ... 
doi:10.1137/0220008 fatcat:4jd3f4rgcngj5n66qypio5sgmu

Random walks on weighted graphs and applications to on-line algorithms

Don Coppersmith, Peter Doyle, Prabhakar Raghavan, Marc Snir
1993 Journal of the ACM  
We study the design and analysis of randomized on-line algorithms. We show that this problem is closely related to the synthesis of random walks on graphs with positive real costs on their edges.  ...  We develop a theory for the synthesis of such w alks, and employ it to design competitive on-line algorithms.  ...  Acknowledgements We thank Allan Borodin and Gil Strang for their helpful comments and suggestions.  ... 
doi:10.1145/174130.174131 fatcat:eww5qvq3a5eszgtgpolhiurmym

The CNN Problem and Other k-Server Variants [chapter]

Elias Koutsoupias, David Scot Taylor
2000 Lecture Notes in Computer Science  
In particular, no memoryless randomized algorithm can be competitive.  ...  The CNN problem contains as special cases two important problems: the BRIDGE problem, also known as the cow-path problem, and the weighted 2-server problem in which the 2 servers may have di erent speeds  ...  Acknowledgements We thank the anonymous referees for their helpful, in-depth comments.  ... 
doi:10.1007/3-540-46541-3_48 fatcat:57qxfstqnvh3xpqjrpsoz7nyle

The CNN problem and other k-server variants

Elias Koutsoupias, David Scot Taylor
2004 Theoretical Computer Science  
In particular, no memoryless randomized algorithm can be competitive.  ...  The CNN problem contains as special cases two important problems: the BRIDGE problem, also known as the cow-path problem, and the weighted 2-server problem in which the 2 servers may have di erent speeds  ...  Acknowledgements We thank the anonymous referees for their helpful, in-depth comments.  ... 
doi:10.1016/j.tcs.2004.06.002 fatcat:pthcfaqq3jhp3f55mws6dgncyq

Random walks on weighted graphs, and applications to on-line algorithms

D. Coppersmith, P. Doyle, P. Raghavan, M. Snir
1990 Proceedings of the twenty-second annual ACM symposium on Theory of computing - STOC '90  
We study the design and analysis of randomized on-line algorithms. We show that this problem is closely related to the synthesis of random walks on graphs with positive real costs on their edges.  ...  We develop a theory for the synthesis of such walks, and employ it to design competitive on-line algorithms.  ...  Acknowledgements We thank Allan Borodin and Gil Strang for their helpful comments and suggestions.  ... 
doi:10.1145/100216.100266 dblp:conf/stoc/CoppersmithDRS90 fatcat:sumfy2hprzbyjmc2qobtfzpz5m

On-Line Load Balancing in a Hierarchical Server Topology

Amotz Bar-Noy, Ari Freund, Joseph (Seffi) Naor
2001 SIAM journal on computing (Print)  
We also show a lower bound of 3 for the unweighted integral model when temporary jobs are allowed. We generalize the problem and consider hierarchies in which the servers form a tree.  ...  We show a lower bound of e for the unweighted case (both integral and fractional). This bound is valid even with respect to randomized algorithms.  ...  Note that the assignment generated by a uniform memoryless algorithm is independent of both the number of servers and the order of jobs in the input.  ... 
doi:10.1137/s0097539798346135 fatcat:62jdjgj2lfb3zlhlhjjqfz7bqy

The server problem and on-line games [chapter]

Marek Chrobak, Lawrence Larmore
1992 DIMACS Series in Discrete Mathematics and Theoretical Computer Science  
The General Work Function Algorithm. In Section 2.3 we introduced for the k-server problem. The concept generalizes naturally to a wide collection of on-line problems.  ...  Lemma 2. 3 3 If M is a metric space, and if M embeds isometrically in M , and if there is a c-competitive algorithm for the k-server problem in M , then there is a c-competitive algorithm for the k-server  ... 
doi:10.1090/dimacs/007/02 dblp:conf/dimacs/ChrobakL91 fatcat:ytpmuwe6yvcxtevn2pmpjjtemq

The Randomized Competitive Ratio of Weighted k-server is at least Exponential [article]

Nikhil Ayyadevara, Ashish Chiplunkar
2021 arXiv   pre-print
The weighted k-server problem is a natural generalization of the k-server problem in which the cost incurred in moving a server is the distance traveled times the weight of the server.  ...  In this article, we make significant progress towards understanding the randomized competitive ratio of weighted k-server on uniform metrics.  ...  It is, in fact, a randomized memoryless algorithm generalizing the algorithm by Chrobak and Sgall [7] for k = 2, and it achieves the competitive ratio against a stronger form of adversary called adaptive  ... 
arXiv:2102.11119v3 fatcat:gauufckwarafdd3s2i3z7og74i

Design of On-Line Algorithms Using Hitting Times

Prasad Tetali
1999 SIAM journal on computing (Print)  
Besides providing new insight into random walks on weighted graphs, we show how these identities give us a way of designing competitive randomized on-line algorithms for certain well-known problems.  ...  Random walks are well known for playing a crucial role in the design of randomized off-line as well as on-line algorithms.  ...  The author would also like to thank Mike Saks (the no-longer-anonymous referee) for a careful reading and constructive criticism of the manuscript.  ... 
doi:10.1137/s0097539798335511 fatcat:ke2weubvivdqfdyb54qpvzn6eu

Page 1283 of Mathematical Reviews Vol. , Issue 2001B [page]

2001 Mathematical Reviews  
Then we give a ve competitive algorithm for the (6,3)-server problem on the real line. Our algorithm is simple and memoryless.  ...  We consider a more general problem called the (k,/)-server problem, in which a request is served using / out of k available servers.  ... 
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