Abstract
We consider online algorithms with respect to the competitive ratio. In this paper, we explore one-way automata as a model for online algorithms. We focus on quantum and classical online algorithms. For a specially constructed online minimization problem, we provide a quantum log-bounded automaton that is more effective (has less competitive ratio) than classical automata, even with advice, in the case of the logarithmic size of memory. We construct an online version of the well-known Disjointness problem as a problem. It was investigated by many researchers from a communication complexity and query complexity point of view.
Highlights
In the paper, we discuss a computational model used to solve optimization problems
We focus on online algorithms that many researchers explore
We can say that an online algorithm solves an online minimization problem
Summary
We discuss a computational model used to solve optimization problems. We focus on online algorithms that many researchers explore. An online algorithm processes an input data stream and outputs a data stream in an online fashion. It should return a piece of output variables immediately after reading a piece of input variables. We can say that an online algorithm solves an online minimization problem. Researchers consider different measures of effectiveness for online algorithms [1,2]. If we consider the cost of the output generated by an online algorithm and the cost of the output produced by an optimal offline algorithm, the competitive ratio is the ratio of these to costs. If the ratio is at most c in the worst case, we call the algorithm c-competitive. We can say that the competitive ratio of the algorithm is c
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