The first half of the paper is a general introduction which emphasizes the central role that the PRAM model of parallel computation plays in algorithmic studies for parallel computers. Some of the collective knowledge-base on non-numerical parallel algorithms can be characterized in a structural way. Each structure relates a few problems and technique to one another from the basic to the more involved. The second half of the paper provides a bird's-eye view of such structures for: (1) list, tree and graph parallel algorithms; (2) very fast deterministic parallel algorithms; and (3) very fast randomized parallel algorithms. 1 Introduction Parallelism is a concern that is missing from "traditional" algorithmic design. Unfortunately, it turns out that most efficient serial algorithms become rather inefficient parallel algorithms. The experience is that the design of parallel algorithms requires new paradigms and techniques, offering an exciting intellectual challenge. We note that it had...

A hash table is a representation of a set in a linear size data structure that supports constanttime membership queries. We show how to construct a hash table for any given set of n keys in O(lg lg n) parallel time with high probability, using n processors on a weak version of a crcw pram. Our algorithm uses a novel approach of hashing by "oblivious execution" based on probabilistic analysis to circumvent the parity lower bound barrier at the near-logarithmic time level. The algorithm is simple and is sketched by the following: 1. Partition the input set into buckets by a random polynomial of constant degree. 2. For t := 1 to O(lg lg n) do (a) Allocate M t memory blocks, each of size K t . (b) Let each bucket select a block at random, and try to injectively map its keys into the block using a random linear function. Buckets that fail carry on to the next iteration. The crux of the algorithm is a careful a priori selection of the parameters M t and K t . The algorithm uses only O(lg lg...