Parallel construction of binary trees with near optimal weighted path length

Abstract

We present parallel algorithms to construct binary trees with almost optimal weighted path length. Specifically, assuming that weights are normalized (to sum up to one) and error refers to the (absolute) difference between the weighted path length of a given tree and the optimal tree with the same weights, we present anO (logn)-time andn(log lognl logn)-EREW-processor algorithm which constructs a tree with error less than 0.18, andO (k logn log^* n)-time andn-CREW-processor algorithm which produces a tree with error at most l/n ^k, and anO (k ² logn)-time andn ²-CREW-processor algorithm which produces a tree with error at most l/n ^k. As well, we describe two sequential algorithms, anO(kn)-time algorithm which produces a tree with error at most l/n ^k, and anO(kn)-time algorithm which produces a tree with error at most$1/2^{n2^k }$. The last two algorithms use different computation models.