On the List Update Problem with Advice.

Joan Boyar, Shahin Kamali, Kim S. Larsen, and Alejandro López-Ortiz.
Information and Computation, 253(3): 411-423, 2017.

We study the online list update problem under the advice model of computation. Under this model, an online algorithm receives partial information about the unknown parts of the input in the form of some bits of advice generated by a benevolent offline oracle. We show that advice of linear size is required and sufficient for a deterministic algorithm to achieve an optimal solution or even a competitive ratio better than 15/14. On the other hand, we show that surprisingly two bits of advice are sufficient to break the lower bound of 2 on the competitive ratio of deterministic online algorithms and achieve a deterministic algorithm with a competitive ratio of 1.6. In this upper-bound argument, the bits of advice determine the algorithm with smaller cost among three classical online algorithms, Timestamp and two members of the MoveToFrontTwo family of algorithms. We also show that MoveToFrontTwo algorithms are 2.5-competitive.

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