# Competitive algorithms for the weighted server problem

@article{Fiat1993CompetitiveAF, title={Competitive algorithms for the weighted server problem}, author={Amos Fiat and Moty Ricklin}, journal={[1993] The 2nd Israel Symposium on Theory and Computing Systems}, year={1993}, pages={294-303} }

The authors deal with a generalization of the k-server problem, in which the servers are unequal. In the weighted server model each of the servers is assigned a positive weight. The cost associated with moving a server equals the product of the distance traversed and the server weight. A weighted k-server algorithm is called competitive if the competitive ratio depends only upon the number of servers. (i.e., the competitive ratio is independent of the weights associated with the servers and the…

## 37 Citations

### 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.

### Competitive Algorithms for Generalized k-Server in Uniform Metrics

- Computer Science, MathematicsSODA
- 2018

The generalized k-server problem is considered in uniform metrics and the first f(k)-competitive algorithms for general k are given, including a deterministic and randomized algorithms with competitive ratio $O(k 2^k)$ and $O (k^3 \log k)$ respectively.

### Weighted k-Server Bounds via Combinatorial Dichotomies

- Computer Science, Mathematics2017 IEEE 58th Annual Symposium on Foundations of Computer Science (FOCS)
- 2017

A doubly exponential lower bound on the competitive ratio of any deterministic online algorithm, that essentially matches the known upper bounds for the problem and closes a large and long-standing gap.

### The k-Server Problem and Fractional Analysis

- Mathematics, Computer Science
- 2005

It is shown that on the line and circle, the randomized version of the k-server problem is equivalent to the fractional version, and the cases for which these versions are not equivalent are classified by presenting a fractional algorithm which cannot be simulated by any randomized algorithm.

### The Randomized Competitive Ratio of Weighted $k$-server is at least Exponential

- Mathematics, Computer ScienceESA
- 2021

This paper cuts down the triply exponential gap between the upper and lower bound to a singly exponential gap by proving that the competitive ratio is at least exponential in k, substantially improving on the previously known lower bound of about ln k.

### More on weighted servers or

- Computer Science, Mathematics
- 2003

A general lower bound for trackless algorithms depending on the cost ratio is presented, proving that the proposed algorithm is the best possible trackless algorithm up to a constant factor for any cost ratio.

### 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.

### Online Paging with Heterogeneous Cache Slots

- Mathematics, Computer ScienceArXiv
- 2022

The deterministic upper bound is extended to the weighted variant of All-or-One Paging (a generalization of standard Weighted Paging), showing that it is also Θ(k).

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