On the limited utility of auxiliary information in the list update problem

Abstract

We consider the problem of dynamic reorganization of a linear list, where requests for the elements are generated randomly with fixed probabilities. The objective is to obtain the smallest expected cost per access. It has been shown that when no a-priori information is given on the reference probabilities, the Counter Scheme(CS) provides an optimal reorganization rule which applies to all possible distributions. In this paper we examine strategies which may use partial a priori information on the access probabilities in the list reorganization process. Such useful knowledge may be either the correct relative order of a subset of the items, or the precise values of some of the probabilities. For the first case we show that a slight modification on the original CS bests all realizable policies. However, it turns out that in the last case there exists no such universal optimal policy. For this model we also show that the obvious organization by the Maximum Likelihood estimate may be inferior to the CS, which...