Quantum online algorithms for a model of the request-answer game with a buffer

In this paper, we considered online algorithms as a request-answer game between two players: an adversary that generates input requests and an online algorithm that answers them. A generalized version of the game that has a buffer of limited size was studied. The adversary loads data to the buffer, while the algorithm has random access to elements of the buffer. For the model, quantum and classical (deterministic or randomized) algorithms were a focus of attention. A specific problem and a quantum algorithm that works better than any classical (deterministic or randomized) algorithm, in terms of competitive ratio, were provided. At the same time, for the problem, classical online algorithms in the standard model are equivalent to the classical algorithms in the request-answer game with a buffer model.