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The CNN problem and other k-server variants

Elias Koutsoupias, David Scot Taylor
2004 Theoretical Computer Science  
This is equivalent to the regular k-server problem under the L∞ norm for movement costs. We give a 1 2 k(k + 1) upper bound for the competitive ratio on trees.  ...  We show that any deterministic online algorithm has competitive ratio at least 6 + √ 17. We also show that some successful algorithms for the k-server problem fail to be competitive.  ...  Acknowledgements We thank the anonymous referees for their helpful, in-depth comments.  ... 
doi:10.1016/j.tcs.2004.06.002 fatcat:pthcfaqq3jhp3f55mws6dgncyq

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

Elias Koutsoupias, David Scot Taylor
2000 Lecture Notes in Computer Science  
This is equivalent to the regular k-server problem under the L∞ norm for movement costs. We give a 1 2 k(k + 1) upper bound for the competitive ratio on trees.  ...  We show that any deterministic online algorithm has competitive ratio at least 6 + √ 17. We also show that some successful algorithms for the k-server problem fail to be competitive.  ...  Acknowledgements We thank the anonymous referees for their helpful, in-depth comments.  ... 
doi:10.1007/3-540-46541-3_48 fatcat:57qxfstqnvh3xpqjrpsoz7nyle

The Generalized Work Function Algorithm Is Competitive for the Generalized 2-Server Problem

René Sitters
2014 SIAM journal on computing (Print)  
We show that the generalized work function algorithm, WFA λ , is constant competitive for the generalized 2-server problem.  ...  Further, we give an outline for a possible extension to k ≥ 2 servers and discuss the applicability of our techniques and of the work function algorithm in general.  ...  For ratio for trees is k but it is unknown if the work function algorithm achieves this ratio. See [24] for more background on this.  ... 
doi:10.1137/120885309 fatcat:zfv3ruofe5f2hd6leyqdlstl2i

Double Coverage with Machine-Learned Advice [article]

Alexander Lindermayr, Nicole Megow, Bertrand Simon
2021 arXiv   pre-print
Our main result is a learning-augmented variation of the well-known Double Coverage algorithm for k-server on the line (Chrobak et al., SIDMA 1991) in which we integrate predictions as well as our trust  ...  When given good predictions, we improve upon known lower bounds for online algorithms without advice.  ...  Our contribution We design learning-augmented memory-constrained online algorithms for the 𝑘server problem on the line. Firstly, we de ne some more notation and the precise prediction model.  ... 
arXiv:2103.01640v2 fatcat:adphmsf4mzci5jjulnyeiqyehm

Putting Ridesharing to the Test: Efficient and Scalable Solutions and the Power of Dynamic Vehicle Relocation [article]

Panayiotis Danassis, Marija Sakota, Aris Filos-Ratsikas, Boi Faltings
2022 arXiv   pre-print
We study the optimization of large-scale, real-time ridesharing systems and propose a modular design methodology, Component Algorithms for Ridesharing (CAR).  ...  We evaluate a diverse set of CARs (14 in total), focusing on the key algorithmic components of ridesharing.  ...  𝑘server/taxi Algorithms Many of these algorithms operate by embedding the input metric space X into a distribution 𝜇 over Hierarchical Separated Trees (HSTs) (e.g., the classic double-coverage [Chrobak  ... 
arXiv:1912.08066v3 fatcat:ygioaadihvhitm6yx4gjba2u7y

The generalized work function algorithm is competitive for the generalized 2-server problem [article]

Rene Sitters
2013 arXiv   pre-print
We show that the generalized work function algorithm is constant competitive for the generalized 2-server problem.  ...  Requests arrive one by one and need to be served instantly by at least one of two servers. We consider the general model where the cost function of the two servers may be different.  ...  problem or weighted kserver problem has an f (k)-competitive algorithm for some function f (k).  ... 
arXiv:1110.6600v2 fatcat:hiuboicysvaz5jpp7pd2xkxfiq

Double Coverage with Machine-Learned Advice

Alexander Lindermayr, Nicole Megow, Bertrand Simon, Mark Braverman
2022
Our main result is a learning-augmented variation of the well-known Double Coverage algorithm for k-server on the line (Chrobak et al., SIDMA 1991) in which we integrate predictions as well as our trust  ...  When given good predictions, we improve upon known lower bounds for online algorithms without advice.  ...  of (untrusted) predictions in designing online algorithms for the kserver problem on the line.  ... 
doi:10.4230/lipics.itcs.2022.99 fatcat:2alrmj77obctno7olcvqlwdia4