This paper presents the underlying theory and the performance of a cluster using a new 2-hop network topology. This topology is constructed using a symmetric equation and Singer Difference Sets and is called SymSig. The degree of connections at each node with SymSig is about half compared to previous methods using Singer Difference Sets. A comparison with a cluster of Clos topology shows significant advantages. The worst case congestion in SymSig topology for unicast permutation is 2, where as in Clos it is proportional to the radix of the building block switches used. The number of switches required is smaller by about 25%, the size of the cluster is larger by about 15% and the worst bandwidth is better by about 50% for SymSig. These advantages are retained for peta and exascale systems. Its performance on a set of collectives like exchange-all, shift-all, broadcast-all and all-to-all send/receive shows improvements ranging from 39% to 83%. Its performance on a molecular dynamics application GROMMACS shows improvement of upto 33%. This network is particularly suitable for applications that require global all to all communications. The low latency of this network makes it scaleable and an attractive alternative for building peta and exascale systems.

Parallel Sparse Matrix Vector Multiplication (PSpMV) is a compute intensive kernel used in iterative solvers like Conjugate Gradient, GMRES and Lanzcos. Numerous attempts at optimizing this function have been made that require fine tuning of many hardware and software parameters to achieve optimal performance. We attempt to offer a simple framework that involves (i) Employing a greedy algorithm to extract variable-sized dense sub matrices without zeroes filled in, (ii) Partitioning the sparse matrix in a load balanced manner and maintaining partial information at each node, and (iii) Overlapping communication with computation. Using the aforementioned, we reduce memory traffic and hide communication latencies, and hope to inherently achieve improved cache and register utilization. This paper reports the performance improvements of PSpMV as such and when used in Preconditioned Conjugate Gradient (PCG).

This paper presents a new and systematic method to generate tests for microprocessors. A functional level model for the microprocessor is used and it is represented by a reduced graph. A new and comprehensive model of the instruction execution process is developed. Various types of faults are analyzed and it is shown that with the use of appropriate codewords all faults can be classified into three types. This gives rise to a systematic procedure to generate tests which is independent of the microprocessor implementation details. Tests are given to detect faults in any microprocessor, first for the READ register instructions, and then for the remaining instructions. These tests can be executed by the microprocessor in a self-test mode, thus dispensing with the need for an external tester.