Abstract. The relative worst order ratio is a measure for the quality of online algorithms. Unlike the competitive ratio, it compares algorithms directly without involving an optimal offline algorithm. The measure has been successfully applied to problems like paging and bin packing. In this paper, we apply it to machine scheduling. We show that for preemptive scheduling, the measure separates multiple pairs of algorithms which have the same competitive ratios; with the relative worst order ratio, the algorithm which is “intuitively better " is also provably better. Moreover, we show one such example for non-preemptive scheduling. 1

Abstract. This paper provides a systematic study of several proposed measures for online algorithms in the context of a specific problem, namely, the two server problem on three colinear points. Even though the problem is simple, it encapsulates a core challenge in online algorithms which is to balance greediness and adaptability. We examine Competitive

On-line algorithms are usually analyzed using competitive analysis, in which the performance of an on-line algorithm on a sequence is normalized by the performance of the optimal off-line algorithm on that sequence. In this paper we introduce cooperative analysis as an alternative general framework for the analysis of on-line algorithms. The idea is to normalize the performance of an on-line algorithm by a measure other than the performance of the off-line optimal algorithm OPT. We show that in many instances the perform of OPT on a sequence is a coarse approximation of the difficulty or complexity of a given input. Using a finer, more natural measure we can separate paging and list update algorithms which were otherwise indistinguishable under the classical model. This creates a performance hierarchy of algorithms which better reflects the intuitive relative strengths between them. Lastly, we show that, surprisingly, certain randomized algorithms which are superior to MTF in the classical model are not so in the cooperative case, which matches experimental results. This confirms that the ability of the on-line cooperative algorithm to ignore pathological worst cases can lead to algorithms that are more efficient in practice.