On the List Update Problem with Advice

Joan Boyar, Shahin Kamali, Kim Skak Larsen, Alejandro López-Ortiz

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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 Mtf2 family of algorithms. We also show that Mtf2
algorithms are 2.5-competitive.
Original languageEnglish
JournalInformation and Computation
Issue numberPart 3
Pages (from-to)411-423
Publication statusPublished - 2017


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