High Performance Issues on Parallel Architectures

In an effort to reduce communication latency in mesh-type architectures, these architectures have been augmented by various types of global and reconfigurable bus structures. The static bus structures provide excellent performance in many areas of computation especially structured numerical computations, but they lack the flexibility required of many large numerical and non-numerical applications. Reconfigurable bus systems have the dynamic adaptability to handle a much wider range of applications. While reconfigurable meshes can often yield constant time results for many problems, the cost of this performance is paid in the number of processors required. While in actuality the majority of these processors are employed as switching elements for the bus system and often do little actual computation. In an effort to reduce the processor cost while maintaining performance and communication flexibility, we present a new hybrid parallel array architecture with the goal of optimizing the best features of arrays with global buses and arrays with reconfigurable bus systems. The result is an architecture of n processing elements and a bus interconnection network which requires very basic circuitry to construct and control. This architecture allows prefix computations, such as prefix sum, prefix maximum(minimum) to be accomplished in O(log n) time. These functions then form the building blocks for complex procedures, which more fully exploit the communication flexibility of the architecture. Application of the architecture to graph theory produces optimal algorithms for graph properties such as spanning forest bipartiteness, fundamental cycles, bridges and biconnected components. Other optimal algorithms for the more complex least common ancestor and the connected component problems are also presented. By design, all algorithms maintain optimality for very large sparse graphs. We further examine the architecture\u27s ability to handle basic image processing tasks as well as its potential to simulate other parallel architectures and theoretic models

Optimal Greedy Algorithms for Indifference Graphs

A fundamental problem in social sciences and management is understanding and predicting decisions made by individuals, various groups, or the society as a whole. In this context, one important concept is the notion of indifference. We characterize the class of indifference graphs, that is, graphs which arise in the process of quantifying indifference relations. In particular, we show that these graphs are characterized by the existence of a special ordering of their vertices. As it turns out, this ordering leads naturally to optimal greedy algorithms for a number of computational problems, including coloring, finding a shortest path between two vertices, computing a maximum matching, the center, and a Hamiltonian path