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Abstract:
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.
