Elsevier

Theoretical Computer Science

Volume 554, 16 October 2014, Pages 95-108
Theoretical Computer Science

The string guessing problem as a method to prove lower bounds on the advice complexity

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Abstract

The advice complexity of an online problem describes the additional information both necessary and sufficient for online algorithms to compute solutions of a certain quality. In this model, an oracle inspects the input before it is processed by an online algorithm. Depending on the input string, the oracle prepares an advice bit string that is accessed sequentially by the algorithm. The number of advice bits that are read to achieve some specific solution quality can then serve as a fine-grained complexity measure. The main contribution of this paper is to study a powerful method for proving lower bounds on the number of advice bits necessary. To this end, we consider the string guessing problem as a generic online problem and show a lower bound on the number of advice bits needed to obtain a good solution. We use special reductions from string guessing to improve the best known lower bound for the online set cover problem and to give a lower bound on the advice complexity of the online maximum clique problem.

Keywords

Online algorithms
Competitive analysis
Advice complexity
Online set cover
Online clique

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This work is partially funded by the SNF grant 200021–141089.