A parallel list update problem

Abstract

Given a set of n · m elements arranged in n lists of m elements L 1… L n , and a sequence of requests R = R 1 R 2…, where R i is a set of n elements to be retrieved in the lists, we discuss how to execute each R i in parallel. L 1… L n are stored in the shared memory of an n-processor EREW-PRAM. After R i has been executed, the lists are updated with a move to front (MTF) strategy; then R i+1 can be processed. An amortized analysis shows that the proposed algorithm is ( n 2 + 1)-competitive against a static optimal algorithm, while a lower bound 2 n is proved. The use of randomization allows to decrease the competitivity factor to 9 2 n, versus a lower bound 3 2 n.