We present improved competitive on-line algorithms for the page replic
ation problem and concentrate on important network topologies for whic
h algorithms with a constant competitive ratio can be given. We develo
p an optimal randomized on-line replication algorithm for trees and un
iform networks; its competitive ratio is approximately 1.58. This perf
ormance holds against oblivious adversaries. We also give a randomized
memoryless replication algorithm for trees and uniform networks that
is 2-competitive against adaptive on-line adversaries. Furthermore, we
consider on-line replication algorithms for rings and present general
techniques that transform c-competitive algorithms for trees into 2c-
competitive algorithms for rings. As a result we obtain a randomized o
n-line algorithm for rings that is 3.16-competitive. We also derive tw
o 4-competitive on-line algorithms for rings which are either determin
istic or randomized and memoryless. Again, the randomized results hold
against oblivious adversaries. Apart from these techniques, we finall
y give a randomized memoryless replication algorithm for rings that is
4-competitive against adaptive on-line adversaries. (C) 1998 Academic
Press.