Randomization can be as helpful as a glimpse of the future in online computation
Jesper W. Mikkelsen

TL;DR
This paper introduces new direct product theorems that connect randomized online algorithms with advice complexity, significantly improving lower bounds and revealing equivalences between randomness and advice in online computation.
Contribution
It provides a framework translating randomized online algorithm bounds into advice complexity bounds, advancing understanding of advice's power in online algorithms.
Findings
Advice complexity lower bounds for paging and vertex coloring are significantly improved.
Randomization and sublinear advice are shown to be equally powerful for certain online problems.
Several open questions about randomized algorithms are reformulated as advice complexity questions.
Abstract
We provide simple but surprisingly useful direct product theorems for proving lower bounds on online algorithms with a limited amount of advice about the future. As a consequence, we are able to translate decades of research on randomized online algorithms to the advice complexity model. Doing so improves significantly on the previous best advice complexity lower bounds for many online problems, or provides the first known lower bounds. For example, if is the number of requests, we show that: (1) A paging algorithm needs bits of advice to achieve a competitive ratio better than , where is the cache size. Previously, it was only known that bits of advice were necessary to achieve a constant competitive ratio smaller than . (2) Every -competitive vertex coloring algorithm must use bits of…
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