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In this paper, we analyze and compare the performance on a hypercube multiprocessor of some of the major multigrid techniques used in practice. The model problem considered here is that of solving the 2-D incompressible Navier-Stokes equations representing the flow between two parallel plates. Results obtained by implementing the different multigrid schemes on an iPSC are presented. Effects on the overall performance of various parameters of the algorithms, of the partitioning strategies employed, and of some of the characteristics of the underlying architecture are discussed.

In this paper, we analyze and compare the performance on a hypercube multiprocessor of some of the major multigrid techniques used in practice. The model problem considered here is that of solving the 2-D incompressible Navier-Stokes equations representing the flow between two parallel plates. Results obtained by implementing the different multigrid schemes on an iPSC are presented. Effects on the overall performance of various parameters of the algorithms, of the partitioning strategies employed, and of some of the characteristics of the underlying architecture are discussed.

This paper examines several ways of implementing multigrid algorithms on the hypercube multiprocessor. We consider both the standard multigrid algorithms and a concurrent version proposed by Gannon and Van Rosendale. We present several mappings of the mesh points onto the nodes of the cube. The main property of these mappings, which are based on binary reflected Gray codes, is that the distance between neighboring grid points remains constant from one grid level to another. This results in a communication effective implementation of multigrid algorithms on the hypercube multiprocessor. The hierarchy of grids in multigrid algorithms presents a speical challenge in minimizing the communicaton overhead in a parallel implementation. For even though it is possible to map the grid points of the finest grid onto many architectures such that neighboring grid points are mapped into neighboring processors, it is generally much more difficult to preserve this proximity property for the coarser grids required in the multigrid algorithms.

The process of effectively coordinating and controlling resources during a military engagement is known as Battle Management/ Command, Control, and Communications (BM/C3). One key task of BM/C3 is allocating weapons to destroy targets. The focus of this research is on developing parallel methods to achieve fast and cost effective assignment of weapons to targets. Using the sequential Hungarian method for solving the assignment problem as a basis, this report presents the development and relative performance comparison of four parallel assignment algorithms implemented on the Intel iPSC hypercube computer. The first approach partitions the problem space into smaller, independent subproblems and assigns each to a processing node in the hypercube. The second and third approaches also partition the problem space, but they assign each partition to a group of processing nodes. Each group is controlled by a separate node which further subdivides the partition among members of the group. In the second approach, the control node acts as an arbitrator to eliminate the redundant assignment of weapons to targets by idling redundantly allocated weapons. The third approach eliminates redundant weapon allocations by selecting the least costly redundant allocations and directing additional processing to reallocate the more costly weapons. The fourth approach is a parallel implementation of the Hungarian algorithm, where certain subtasks are performed in parallel. This approach produces an optimal assignment instead of the sub-optimal assignment generally obtained using either of the three heuristic approaches.

112 p. 28 cm

This paper presents algorithms for labeling the connected components of a binary image using a hypercube or shuffle-exchange computer. The algorithms label the components of an sq 1 + N x sq 1 + N pixel image in O(long sq of N) time using a hypercube or shuffle-exchange computer with N processors and a constant amount of memory per processor. The algorithms that are presented are the first to solve this problem in O(log sq of N) time. The algorithms are based on a divide-and-conquer approach and use as a subroutine an O(log N) time PRAM algorithm for labeling the connected components of a graph. The simulation of the PRAM by the hypercube and shuffle-exchange computers is particularly efficient because the PRAM that is being simulated has only O(N to the 3/4 power) processors and memory cells. Keywords: Parallel algorithms; Image processing; Hypercube; Shuffle exchange; Connected component labeling.

We investigate a set of discrete-time quantum search algorithms on the n-dimensional hypercube following a proposal by Shenvi, Kempe and Whaley. We show that there exists a whole class of quantum search algorithms in the symmetry reduced space which perform a search of a marked vertex in time of order $\sqrt{N}$ where $N = 2^n$, the number of vertices. In analogy to Grover's algorithm, the spatial search is effectively facilitated through a rotation in a two-level sub-space of the full Hilbert space. In the hypercube, these two-level systems are introduced through avoided crossings. We give estimates on the quantum states forming the 2-level sub-spaces at the avoided crossings and derive improved estimates on the search times.

The purpose of this grant was to purchase a hypercube computer to support DoD-sponsored research, and other research, in parallel numerical computation. The plans that were outlined in the proposal were followed very closely. We have purchased a 32-node Intel iPSC-D5 hypercube computer with the funds from this grant, and have used the matching University contribution to support the maintenance of this computer. This computer has been used, over the past year, for research in parallel numerical computation in areas including global optimization, VLSI design, large sparse systems of linear equations, and eigenvalue problems, as well as for research in the languages for parallel computation and in the debugging and measurement of parallel programs.

Genetic algorithms are stochastic search algorithms which model natural adaptive systems. In support of the development of a genetic search package for AFIT's iPSC/2 Hypercube, this study focused on two problem areas associated with hypercube implementations. Premature convergence occurs when the population becomes dominated by locally optimal, but globally inferior, solutions. Based on an examination of past hypercube implementations, the selection and communication strategies were hypothesized as causes of premature convergence. Experiments to test these hypotheses were conducted on Rosenbrock's saddle, a function often associated with premature convergence. Communication of best solutions led to premature convergence in small population sizes, but increased the likelihood of finding the global optimal in large population sizes. Genetic algorithms using global selection were more robust than those using local selection. GA-hard problems are intrinsically difficult for standard genetic algorithms. Messy genetic algorithms are effective against GA-hard problems. The second part of this study added a parallel version of a messy genetic algorithm to the genetic algorithm package. Against a sample GA-hard problem, the parallel implementation achieved a linear speedup of the sequential bottleneck while still finding the global optimal. The messy genetic algorithm should be applied to problems of practical importance. Genetic algorithms, Hypercube.