An asymptotic optimality of the transposition rule for linear lists

The linear list is one of basic data structures in computer science with search being a primary operation defined on it. Items are located in the list by sequentially examining them from the beginning of the list. Intuitively one would like to place items that are frequently requested at the front of the list in order to minimize the number of items being examined. Given the properties of the request sequence one could place items in an order that minimizes the search cost. Yet often properties of the request sequence are either not known in advance or time dependent. Hence, it is desirable to employ self-organizing algorithms. The two best known such rules are the move-to-front and transposition rule [9, Section 6]. In addition to being simple these rules are memory-free, i.e., require no memory for their operation.