Mapping Parallel Iterative Algorithms onto Workstation Networks

For communication-intensive parallel applications, the maximum degree of concurrency achievable is limited by the communication throughput made available by the network. In previous work [HPS94], we showed experimentally that the performance of certain parallel applications running on a workstation network can be improved significantly if a congestion control protocol is used to enhance network performance. In this paper, we characterize and analyze the communication requirements of a large class of supercomputing applications that fall under the category of fixed-point problems, amenable to solution by parallel iterative methods. This results in a set of interface and architectural features sufficient for the efficient implementation of the applications over a large-scale distributed system. In particular, we propose a direct link between the application and network layer, supporting congestion control actions at both ends. This in turn enhances the system's responsiveness to network congestion, improving performance. Measurements are given showing the efficacy of our scheme to support large-scale parallel computations.

Geometric Generalizations of the Power of Two Choices

A well-known paradigm for load balancing in distributed systems is the``power of two choices,''whereby an item is stored at the less loaded of two (or more) random alternative servers. We investigate the power of two choices in natural settings for distributed computing where items and servers reside in a geometric space and each item is associated with the server that is its nearest neighbor. This is in fact the backdrop for distributed hash tables such as Chord, where the geometric space is determined by clockwise distance on a one-dimensional ring. Theoretically, we consider the following load balancing problem. Suppose that servers are initially hashed uniformly at random to points in the space. Sequentially, each item then considers d candidate insertion points also chosen uniformly at random from the space,and selects the insertion point whose associated server has the least load. For the one-dimensional ring, and for Euclidean distance on the two-dimensional torus, we demonstrate that when n data items are hashed to n servers,the maximum load at any server is log log n / log d + O(1) with high probability. While our results match the well-known bounds in the standard setting in which each server is selected equiprobably, our applications do not have this feature, since the sizes of the nearest-neighbor regions around servers are non-uniform. Therefore, the novelty in our methods lies in developing appropriate tail bounds on the distribution of nearest-neighbor region sizes and in adapting previous arguments to this more general setting. In addition, we provide simulation results demonstrating the load balance that results as the system size scales into the millions.

How Good are Genetic Algorithms at Finding Large Cliques: An Experimental Study

This paper investigates the power of genetic algorithms at solving the MAX-CLIQUE problem. We measure the performance of a standard genetic algorithm on an elementary set of problem instances consisting of embedded cliques in random graphs. We indicate the need for improvement, and introduce a new genetic algorithm, the multi-phase annealed GA, which exhibits superior performance on the same problem set. As we scale up the problem size and test on \hard" benchmark instances, we notice a degraded performance in the algorithm caused by premature convergence to local minima. To alleviate this problem, a sequence of modi cations are implemented ranging from changes in input representation to systematic local search. The most recent version, called union GA, incorporates the features of union cross-over, greedy replacement, and diversity enhancement. It shows a marked speed-up in the number of iterations required to find a given solution, as well as some improvement in the clique size found. We discuss issues related to the SIMD implementation of the genetic algorithms on a Thinking Machines CM-5, which was necessitated by the intrinsically high time complexity (O(n3)) of the serial algorithm for computing one iteration. Our preliminary conclusions are: (1) a genetic algorithm needs to be heavily customized to work "well" for the clique problem; (2) a GA is computationally very expensive, and its use is only recommended if it is known to find larger cliques than other algorithms; (3) although our customization e ort is bringing forth continued improvements, there is no clear evidence, at this time, that a GA will have better success in circumventing local minima.