Comparison of self-organizing linear search rules

Abstract

Consider a file with n records denoted by R1, R2, …, Rn. At each access of a record, the file has to be searched sequentially and it is assumed that the search cost is proportional to the number of probes needed to retrieve the records. The access probabilities p1, p2, …, pn are assumed to be unknown constants and accesses are assumed to be independent. A move-forward self-organizing rule moves a record accessed in the ith position to the lith position without changing the relative ordering of other records where li, = 1, li, < i for i = 2, …, n and li+1≧li. A move-forward rule R is said to be ≦ another move-forward rule R′ if l′i≦li for all i. It is shown that when p2 = p3 = ··· = pn, R ≦ R′, implies cost R ≦ cost R′. This is a generalization of some known results. A new consequence is that the move-up-k + 1 rule is more costly than the move-up-k rule and the move-to-front rule is the most costly of all move-forward rules.