Representing shared data on distributed-memory parallel computers

The problem of representing a set (Formula presented) of read-write variables on an n-node distributed-memory parallel computer is considered. It is shown that U can be represented among the n nodes of a variant of the mesh of trees using O((m/n) polylog(m/n)) storage per node such that any n-tuple of variables may be accessed in O (log n (log log n)²) time in the worst case for m polynomial in n.