Two New Families of List Update Algorithms

We consider the online list accessing problem and present a new family of competitive-optimal deterministic list update algorithms which is the largest class of such algorithms known to-date. This family, called Sort-by-Rank (sbr), is parametrized with a real 0 1, where sbr(0) is the Move-to-Front algorithm and sbr(1) is equivalent to the Timestamp algorithm. The behaviour of sbr() mediates between the eager strategy of Move-to-Front and the more conservative behaviour of Timestamp. We also present a family of algorithms Sort-by-Delay (sbd) which is parametrized by the positive integers, where sbd(1) is Move-to-Front and sbd(2) is equivalent to Timestamp. In general, sbd(k) is k-competitive for k 2. This is the rst class of algorithms that is asymptotically optimal for independent, identically distributed requests while each algorithm is constant-competitive. Empirical studies with with both generated and real-world data are also included.