Elias Koutsoupias
Professor of Computer Science
University of Athens
Panepistimiopolis, Ilissia
Athens 15784
Greece

phone: +30 210 7275122
fax: +30 210 7275114

M. Chrobak, E. Koutsoupias, and J. Noga. More on Randomized On-line Algorithms for Caching. Theoretical Computer Science. 290(3): 1997-2008, 2003.

### Abstract

We address the tradeoff between the competitive ratio and the resources used by randomized on-line algorithms for caching. Two algorithms reported in the literature that achieve the optimal ratio $H_k$ require a lot of memory and perform extensive computation at each step. On the other hand, a very simple algorithm called RMARK has competitive ratio $2H_k-1$, within a factor of $2$ of the optimum. A natural question that arises here is whether there is a tradeoff between simplicity and the competitive ratio. In particular, is it possible to achieve a competitive ratio better than $2H_k-1$ with a simple algorithm like RMARK? We first consider marking algorithms that are natural generalizations of RMARK, and we prove that, for any $\epsilon > 0$, there is no randomized marking algorithm for caching with competitive ratio $(2-\epsilon)H_k$. Thus RMARK is essentially optimal among marking algorithms. Another model of simple caching algorithms is that of trackless algorithms. These are algorithms that do not store any information about items that are not in the cache. It is known that, for $k=2$, there is no randomized trackless algorithm for caching with ratio better than $37/24\approx 1.5416$. The trivial upper bound is $2$, achieved even by deterministic algorithms LRU and FIFO. We reduce this gap by giving a trackless randomized algorithm with competitive ratio $\onefourth(3 + \sqrt{13}) \approx 1.6514$.

### Bib

@Article{CKN03,
author =       {M. Chrobak and E. Koutsoupias and J. Noga},
title =        {More on Randomized On-line Algorithms for Caching},
journal =      {Theoretical Computer Science},
year =         2003,
volume =	 290,
number =	 3,
pages =        {1997--2008}
}