Online Bounded Analysis

Abstract

Though competitive analysis is often a very good tool for the analysis of online algorithms, sometimes it does not give any insight and sometimes it gives counter-intuitive results. Much work has gone into exploring other performance measures, in particular targeted at what seems to be the core problem with competitive analysis: the comparison of the performance of an online algorithm is made with respect to a too powerful adversary. We consider a new approach to restricting the power of the adversary, by requiring that when judging a given online algorithm, the optimal offline algorithm must perform at least as well as the online algorithm, not just on the entire final request sequence, but also on any prefix of that sequence. This is limiting the adversary's usual advantage of being able to exploit that it knows the sequence is continuing beyond the current request. Through a collection of online problems, including machine scheduling, bin packing, dual bin packing, and seat reservation, we investigate the significance of this particular offline advantage.

Relative Worst-Order Analysis: A Survey

“…In chronological order, the main contributions are the following: online/online ratio [45], statistical adversary [61], loose competitive ratio [65], max/max ratio [9], access graphs (incorporating locality of reference) [13], random-order ratio [53], accommodating ratio [25], extra resource analysis [51], diffuse adversary [54], accommodating function [28], smoothed analysis [63], working set (incorporating locality of reference) [2], relative worst-order analysis [18,21], bijective and average analysis [5], relative interval analysis [37], bijective ratio [6], and online-bounded analysis [16,15].…”