On the Competitive Theory and Practice of Online List Accessing Algorithms

Abstract

This paper concerns the online list accessing problem. In the first part of the paper we present two new families of list accessing algorithms. The first family is of optimal, 2-competitive, deterministic online algorithms. This family, called the MRI (MOVE-TO-RECENT-ITEM) family, includes as members the well-known MOVE-TO-FRONT (MTF) algorithm and the recent, more ``conservative'' algorithm TIMESTAMP due to Albers. So far MOVE-TO-FRONT and TIMESTAMP were the only algorithms known to be optimal in terms of their competitive ratio. This new family contains a sequence of algorithms { A(i) } <sub>i \geq 1</sub> where A(1) is equivalent to TIMESTAMP and the limit element A(∈fty) is \mtf. Further, in this class, for each i , the algorithm A(i) is more conservative than algorithm A(i+1) in the sense that it is more reluctant to move an accessed item to the front, thus giving a gradual transition from the conservative TIMESTAMP to the ``reckless'' MTF. The second new family, called the PRI (PASS-RECENT-ITEM) family, is also infinite and contains TIMESTAMP. We show that most algorithms in this family attain a competitive ratio of 3.

In the second, experimental, part of the paper we report the results of an extensive empirical study of the performances of a large set of online list accessing algorithms (including members of our MRI and PRI families). The algorithms' access cost performances were tested with respect to a number of different request sequences. These include sequences of independent requests generated by probability distributions and sequences generated by Markov sources to examine the influence of locality. It turns out that the degree of locality has a considerable influence on the algorithms' absolute and relative costs, as well as on their rankings. In another experiment we tested the algorithms' performances as data compressors in two variants of the compression scheme of Bentley et al. In both experiments, members of the MRI and PRI families were found to be among the best performing algorithms.