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 E REW P RAM algorithms for computing accumulations on trees taking O(log n) time on O(n/log n) processors, which is optimal.

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