# A Randomized Algorithm for Two Servers on the Line (Extended Abstract)

@inproceedings{Bartal1998ARA, title={A Randomized Algorithm for Two Servers on the Line (Extended Abstract)}, author={Yair Bartal and Marek Chrobak and Lawrence L. Larmore}, booktitle={ESA}, year={1998} }

In the k-server problem we wish to minimize, in an online fashion, the movement cost of k servers in response to a sequence of requests. For 2 servers, it is known that the optimal deterministic algorithm has competitive ratio 2, and it has been a long-standing open problem whether it is possible to improve this ratio using randomization. We give a positive answer to this problem when the underlying metric space is a real line, by providing a randomized online algorithm for this case with…

## 10 Citations

A randomized algorithm for two servers in cross polytope spaces

- Mathematics, Computer ScienceTheor. Comput. Sci.
- 2007

Randomized Memoryless Algorithms for the Weighted and the Generalized k-server Problems

- Computer Science, MathematicsACM Trans. Algorithms
- 2020

A framework for working with potential functions defined implicitly as the solution of a linear system is developed and tight bounds on the competitive ratio achievable by randomized memoryless algorithms for the weighted k-server problem on uniform metrics are established.

On Randomized Memoryless Algorithms for the Weighted K-Server Problem

- Computer Science2013 IEEE 54th Annual Symposium on Foundations of Computer Science
- 2013

This work proves that there is an α<sub>k</sub> competitive memoryless algorithm for the weighted k-server problem on uniform spaces, and develops a framework to bound from above the competitive ratio of any randomized memoryless algorithms for this problem.

Randomized Competitive Analysis for Two-Server Problems

- Mathematics, Computer ScienceESA
- 2008

We prove that there exits a randomized online algorithm for the 2-server 3-point problem whose expected competitive ratio is at most 1.5897. This is the first nontrivial upper bound for randomized…

Randomized Competitive Analysis for Two Server Problems

- Mathematics, Computer ScienceAlgorithms
- 2008

We prove that there exists a randomized online algorithm for the 2-server 3-point problem whose expected competitive ratio is at most 1.5897. This is the first nontrivial upper bound for randomized…

R-LINE: A better randomized 2-server algorithm on the line

- Computer Science, MathematicsTheor. Comput. Sci.
- 2012

Knowledge State Algorithms

- Computer ScienceAlgorithmica
- 2009

The novel concept of knowledge states, which consists of a distribution of states for the algorithm, together with a work function which approximates the conditional obligations of the adversary, are introduced.

SIGACT news online algorithms column 13: 2007 - an offine perspective

- Computer ScienceSIGA
- 2008

This is a survey of last year's work on online competitive algorithms, including those from SODA, FOCS, STOC, STACS, COCOON, IsAAC, ESA, ICALP, WAOA, and ISAAC.

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