Results 1 
2 of
2
More on Randomized Online Algorithms for Caching
"... We address the tradeo between the competitive ratio and the resources used by randomized online 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 s ..."
Abstract

Cited by 3 (2 self)
 Add to MetaCart
We address the tradeo between the competitive ratio and the resources used by randomized online 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 tradeo 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 rst consider marking algorithms that are natural generalizations of RMARK, and we prove that, for any > 0, there is no randomized marking algorithm for caching with competitive ratio (2 )H k . Thus RMARK is essentially optimal among marking algorithms.
More on randomized online algorithms for caching: simplicity vs competitiveness
 Department of Computer Science and Engineering, University of California, Riverside
, 2001
"... We address the tradeoff between the competitive ratio and the resources used by randomized online algorithms for caching. Two algorithms reported in the literature that achieve the optimal ratio Hk require a lot of memory and perform extensive computation at each step. On the other hand, a very sim ..."
Abstract

Cited by 1 (1 self)
 Add to MetaCart
We address the tradeoff between the competitive ratio and the resources used by randomized online algorithms for caching. Two algorithms reported in the literature that achieve the optimal ratio Hk 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 2Hk − 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 2Hk − 1 with a simple algorithm like RMARK? We first consider marking algorithms that are natural generalizations of RMARK, and we prove that, for any ɛ> 0, there is no randomized marking algorithm for caching with competitive ratio (2 − ɛ)Hk. 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 ≈ 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 1 4 (3 + √ 13) ≈ 1.6514.