Mermera: Non-Coherent Distributed Shared Memory for Parallel Computing

The proliferation of inexpensive workstations and networks has prompted several researchers to use such distributed systems for parallel computing. Attempts have been made to offer a shared-memory programming model on such distributed memory computers. Most systems provide a shared-memory that is coherent in that all processes that use it agree on the order of all memory events. This dissertation explores the possibility of a significant improvement in the performance of some applications when they use non-coherent memory. First, a new formal model to describe existing non-coherent memories is developed. I use this model to prove that certain problems can be solved using asynchronous iterative algorithms on shared-memory in which the coherence constraints are substantially relaxed. In the course of the development of the model I discovered a new type of non-coherent behavior called Local Consistency. Second, a programming model, Mermera, is proposed. It provides programmers with a choice of hierarchically related non-coherent behaviors along with one coherent behavior. Thus, one can trade-off the ease of programming with coherent memory for improved performance with non-coherent memory. As an example, I present a program to solve a linear system of equations using an asynchronous iterative algorithm. This program uses all the behaviors offered by Mermera. Third, I describe the implementation of Mermera on a BBN Butterfly TC2000 and on a network of workstations. The performance of a version of the equation solving program that uses all the behaviors of Mermera is compared with that of a version that uses coherent behavior only. For a system of 1000 equations the former exhibits at least a 5-fold improvement in convergence time over the latter. The version using coherent behavior only does not benefit from employing more than one workstation to solve the problem while the program using non-coherent behavior continues to achieve improved performance as the number of workstations is increased from 1 to 6. This measurement corroborates our belief that non-coherent shared memory can be a performance boon for some applications.

An Implementation of Mermera: A Shared Memory System that Mixes Coherence with Non-coherence

Coherent shared memory is a convenient, but inefficient, method of inter-process communication for parallel programs. By contrast, message passing can be less convenient, but more efficient. To get the benefits of both models, several non-coherent memory behaviors have recently been proposed in the literature. We present an implementation of Mermera, a shared memory system that supports both coherent and non-coherent behaviors in a manner that enables programmers to mix multiple behaviors in the same program[HS93]. A programmer can debug a Mermera program using coherent memory, and then improve its performance by selectively reducing the level of coherence in the parts that are critical to performance. Mermera permits a trade-off of coherence for performance. We analyze this trade-off through measurements of our implementation, and by an example that illustrates the style of programming needed to exploit non-coherence. We find that, even on a small network of workstations, the performance advantage of non-coherence is compelling. Raw non-coherent memory operations perform 20-40~times better than non-coherent memory operations. An example application program is shown to run 5-11~times faster when permitted to exploit non-coherence. We conclude by commenting on our use of the Isis Toolkit of multicast protocols in implementing Mermera.

Non-Uniform Reductions

We study properties of non-uniform reductions and related completeness notions. We strengthen several results of Hitchcock and Pavan and give a trade-off between the amount of advice needed for a reduction and its honesty on NEXP. We construct an oracle relative to which this trade-off is optimal. We show, in a more systematic study of non-uniform reductions, that among other things non-uniformity can be removed at the cost of more queries. In line with Post's program for complexity theory we connect such 'uniformization' properties to the separation of complexity classes.