Concurrent processing of linearly ordered data structures on hypercube multicomputers

The paper presents a simple and effective method for the concurrent manipulation of linearly ordered data structures on hypercube systems. The method Is based on the existence of an augmented binomial search tree, called the pruned binomial tree, rooted at any arbitrary processor node of the hypercube such that; every edge of the tree corresponds to a direct link between a pair of hypercube nodes; and the tree spans any arbitrary sequence of n consecutive nodes containing the root, using a fanout of at most [log₂ n] and a depth of at most [log₂ n]+1. Search trees spanning nonoverlapping processor lists are formed using only local information, and can be used concurrently without contention problems. Thus, they can be used for performing operations such as broadcast and merge simultaneously on sets with nonuniform sizes. Extensions of the tree to k-ary n-cubes and faulty hypercubes are presented. Applications of this concurrent data structure to low- and intermediate-level image processing algorithms, and for dictionary operations involving multiple keys, are also outlined