Advice Complexity of the Online Search Problem

TL;DR

This paper investigates the advice complexity of the online search problem, establishing bounds on information needed for competitive ratios and comparing advice to randomization.

Contribution

It introduces an algorithm with advice complexity bounds and provides matching lower bounds, advancing understanding of information requirements in online search.

Findings

Algorithm achieves competitive ratio based on advice bits

Matching lower bounds established for advice complexity

Advice can be as powerful as randomization in this context

Abstract

The online search problem is a fundamental problem in finance. The numerous direct applications include searching for optimal prices for commodity trading and trading foreign currencies. In this paper, we analyze the advice complexity of this problem. In particular, we are interested in identifying the minimum amount of information needed in order to achieve a certain competitive ratio. We design an algorithm that reads b bits of advice and achieves a competitive ratio of (M/m)^(1/(2^b+1)) where M and m are the maximum and minimum price in the input. We also give a matching lower bound. Furthermore, we compare the power of advice and randomization for this problem.