A new measure for the study of on-line algorithms

An accepted measure for the performance of an on-line algorithm is the “competitive ratio“ introduced by Sleator and Tarjan. This measure is well motivated and has led to the development of a mathematical theory for on-line algorithms.We investigate the behavior of this measure with respect to memory needs and benefits of lookahead and find some counterintuitive features. We present lower bounds on the size of memory devoted to recording the past. It is also observed that the competitive ratio reflects no improvement in the performance of an on-line algorithm due to any (finite) amount of lookahead.We offer an alternative measure that exhibits a different and, in some respects, more intuitive behavior. In particular, we demonstrate the use of our new measure by analyzing the tradeoff between the amortized cost of on-line algorithms for the paging problem and the amount of lookahead available to them. We also derive on-line algorithms for theK-server problem on any bounded metric space, which, relative to the new measure, are optimal among all on-line algorithms (up to a factor of 2) and are within a factor of 2K from the optimal off-line performance.