A Polylogarithmic-Competitive Algorithm for the k-Server Problem

@article{Bansal2011APA,
  title={A Polylogarithmic-Competitive Algorithm for the k-Server Problem},
  author={Nikhil Bansal and Niv Buchbinder and Aleksander Madry and Joseph Naor},
  journal={2011 IEEE 52nd Annual Symposium on Foundations of Computer Science},
  year={2011},
  pages={267-276}
}
  • N. Bansal, Niv Buchbinder, J. Naor
  • Published 7 October 2011
  • Computer Science, Mathematics
  • 2011 IEEE 52nd Annual Symposium on Foundations of Computer Science
We give the first polylogarithmic-competitive randomized 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. This improves upon the (2k-1)-competitive algorithm of Koutsoupias and Papadimitriou (J. ACM 1995) whenever n is sub-exponential in k. 
Polylogarithmic Competitive Ratios for the Randomized Online k-server Problem
In this paper, we will study recent work on and progress towards polylogarithmic competitive ratios for the k-server problem. For a long time, the best known competitive ratio that held for general
An O(log k log^2 n)-competitive Randomized Algorithm for the k-Sever Problem
In this paper, we show that there is an O(log k log^2 n)-competitive randomized algorithm for the k-sever problem on any metric space with n points, which improved the previous best competitive ratio
Memoryless Algorithms for the Generalized k-server Problem on Uniform Metrics
TLDR
It is shown that the Harmonic Algorithm achieves this competitive ratio and provides matching lower bounds, which improves the doubly-exponential bound of Chiplunkar and Vishwanathan for the more general setting of uniform metrics with different weights.
A Competitive Ratio Approximation Scheme for the k-Server Problem in Fixed Finite Metrics
TLDR
For each fixed finite metrics, the analysis of a class of online problems that includes the $k-server problem in finite metrics such that the authors only have to consider finite sequences of request qualifies as a competitive ratio approximation scheme as defined by G\"unther et al.
Randomized Online Algorithms with High Probability Guarantees
TLDR
A broad class of online problems is defined that includes some of the well-studied problems like paging, k-server and metrical task systems on finite metrics, and it is shown that for these problems it is possible to obtain another algorithm that achieves the same solution quality up to an arbitrarily small constant error with high probability.
Weighted k-Server Bounds via Combinatorial Dichotomies
TLDR
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.
R-LINE: A better randomized 2-server algorithm on the line
Settling the Randomized k-sever Conjecture on Some Special Metrics
TLDR
The randomized $k-sever conjecture is settled for the following metric spaces: line, circle, Hierarchically well-separated tree (HST), and it is shown that there is an O(\log k)-competitive randomized k-sever algorithm for above metric spaces.
R-LINE: A Better Randomized 2-Server Algorithm on the Line
A randomized on-line algorithm is given for the 2-server problem on the line, with competitiveness less than 1.901 against the oblivious adversary. This improves the previously best known
AN ONLINE ALGORITHM FOR THE 2{SERVER PROBLEM ON THE LINE WITH IMPROVED COMPETITIVENESS
TLDR
This algorithm achieves the lowest competitive ratio of any known randomized algorithm for the 2-server problem on the line, named R–LINE (for Randomized Line), by utilizing ideas from T-theory, game theory, and linear programming.
...
1
2
3
4
5
...

References

SHOWING 1-10 OF 44 REFERENCES
Competitive k-Server Algorithms
Randomized k-server on hierarchical binary trees
We design a randomized online algorithm for k-server on binary trees with hierarchical edge lengths, with expected competitive ratio O(log Delta), where Delta is the diameter of the metric. This is
Randomized algorithm for the k-server problem on decomposable spaces
A General Decomposition Theorem for the k-Server Problem
TLDR
The first general decomposition theorem for the k-server problem is presented, which implies O(polylog(k)-competitive randomized algorithms for certain metric spaces consisting of a polylogarithmic number of widely separated sub-spaces, and takes a first step towards a general O- competitive algorithm.
A polylog(n)-competitive algorithm for metrical task systems
We present a randomized on-line algorithm for the Metrical Task System problem that achieves a competitive ratio of O(log6 n) for arbitrary metric spaces, against an oblivious adversary. This is the
Towards the randomized k-server conjecture: a primal-dual approach
Recently, Coté et al. [10] proposed an approach for solving the k-server problem on Hierchically Separated Trees (HSTs). In particular, they define a problem on a uniform metric, and show that if an
An Optimal On-Line Algorithm for k-Servers on Trees
TLDR
The k-server problem is investigated when the metric space is a tree and an on-line k-competitive algorithm for k-servers is presented that is memoryless, in the sense that it does not use any information from the past.
A decomposition theorem and bounds for randomized server problems
TLDR
The authors prove a lower bound of Omega ( square root logk/loglogk) for the competitive ratio of randomized algorithms for the k-server problem against an oblivious adversary and provides a new lower bound for the metrical task system problem as well.
A Ramsey-type theorem for metric spaces and its applications for metrical task systems and related problems
TLDR
The paper gives a nearly logarithmic lower bound on the randomized competitive ratio for a Metrical Task Systems model and proves that in every metric space there exists a large subspace which is approximately a "hierarchically well- separated tree" (HST) (Y. Bartal, 1996).
...
1
2
3
4
5
...