Techniques for solving graph problems in parallel environments

We introduce new paradigms for the construction of efficient parallel graph algorithms. These paradigms, called filtration and funnelled pipelining, are illustrated with VLSI circuits for computing connected components, minimum spanning forests, and biconnected components. These circuits use realistic I/O schedules and require time and area of O(n1+ε). Thus they are essentially optimal. Filtration is a technique used to rapidly discard irrelevant input data. This greatly reduces storage, time, and communications costs in a wide variety of problems. A funnelled pipeline is obtained by building a series of increasingly thorough filter stages. Transition times along such a pipeline of filters form an exponentially increasing sequence. The increasing amount of time exactly balances the increasing degree of filtration. This balance makes possible the cascaded filtration critical to the minimum spanning forest and the biconnected components algorithms.