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We consider online algorithms as a request-answer game. An adversary thatgenerates input requests, and an online algorithm answers. We consider ageneralized version of the game that has a buffer of limited size. Theadversary loads data to the buffer, and the algorithm has random access toelements of the buffer. We consider quantum and classical (deterministic orrandomized) algorithms for the model.  In the paper, we provide a specific problem (The Most Frequent KeywordProblem) and a quantum algorithm that works better than any classical(deterministic or randomized) algorithm in terms of competitive ratio. At thesame time, for the problem, classical online algorithms in the standard modelare equivalent to the classical algorithms in the request-answer game withbuffer model.

Quantum Request-Answer Game with Buffer Model for Online Algorithms