MPI-I-94-106

The page replication problem arises in the memory management of large multiprocessor systems. Given a network of processors, each of which has its local memory, the problem consists of deciding which local memories should contain copies of pages of data so that a sequence of memory accesses can be accomplished efficiently. We present new competitive on-line algorithms for the page replication problem and concentrate on important network topologies for which algorithms with a constant competitive factor can be given. We develop the first optimal randomized on-line replication algorithm for trees and uniform networks; its competitive factor is approximately 1.58. Furthermore we consider on-line replication algorithms for rings and present general techniques that transform large classes of $c$-competitive algorithms for trees into $2c$-competitive algorithms for rings. As a result we obtain a randomized on-line algorithm for rings that is 3.16-competitive. We also derive two 4-competitive on-line algorithms for rings which are either deterministic or memoryless. All our algorithms improve the previously best competitive factors for the respective topologies.