Efficient Parallel Algorithms for Tree Accumulations

Abstract

Accumulations are higher-order operations on structured objects; they leave the shape of an object unchanged, but replace elements of that object with accumulated information about other elements. Upwards and downwards accumulations on trees are two such operations; they form the basis of many tree algorithms. We present two EREW PRAM algorithms for computing accumulations on trees taking O(\log n) time on O(n/\log n) processors, which is optimal.