FRAMES: A SIMPLE CHARACTERIZATION OF PERMUTATIONS REALIZED BY FREQUENTLY USED NETWORKS

Rearrangeable multistage interconnection networks such as the Benes network realize any permutation, yet their routing algorithms are not cost-effective. On the other hand, non-rearrangeable networks can have inexpensive routing algorithms, but no simple technique exists to characterix all the permutations realized on these netwarks. This paper introduces the concept of frame and shows how iit can be used to characterize all the permutations realized on various multistage inteirconnection networks. They include any subnetwork of the Benes network, the class of networks that are topologically equivalent to the baseline network, and cascaded baseline and shuffle-exchange networks. The question of how the addition of a stage to any of these networks affects the type of permutations realized by the network is precisely answered. Also, of interest from a theoretical standpoint, a new simple proof is provided for the rearrangeability of the Benes network

A case study in synchronous parallel discrete event simulation

This paper considers the suitability of SPED, a synchronous parallel discrete event simulator, for the study of message passing networks. The simulation algorithm is described, and its potential performance is assessed showing that, under some simplifying assumptions, SPED might offer speedups directly proportional to the number of processors used in the simulation. An implementation of SPED in a distributed memory parallel system is used to study a model of an interconnection network for a multicomputer. Experiments show that SPED performs nearly as expected, as long as the event density imposed on the LPs is above a certain threshold. If this is not the case, the overhead due to synchronization plus communication dominates the execution time, and the achieved speedups are not as good. Some ways to improve the performance of SPED are proposed: a method to reduce the number of messages interchanged during the simulation, and a new algorithm for synchronous PDES, called PTD-NB (Parallel Time Driven- No Barriers), which reduces the synchronization overhead by removing barrier operations and can be easily implemented in multicomputer systems without support for global synchronization operations

Dist a distribution independent parallel programs for matrix multiplication

This report considers the problem of writing data distribution independent (DDI) programs in order to eliminate or reduce initial data redistribution overheads for distributed memory parallel computers. The functionality and execution time of DDI programs are independent of initial data distributions. First, modular mappings, which can be used to derive many equally optimal ant1 functionally equivalent programs, are briefly reviewed. Relations between modular mappings and input data distributions are then established. These relations are the basis of a systematic approach to the derivation of DDI programs which is illustrated for matrix-matrix multiplication(c = a x b). Conditions on data distributions that correspond to an optimal modular mapping are: (1) the first row of the inverse of distribution pattern matrix of army \u27a\u27 should be equal to the second row of the inverse of distribution pattern matrix of array \u27b\u27) (2) the second row of the inverse of distribution pattern matrix of array \u27a\u27 should be linearly independent of the first row of the inverse of distribution pattern matrix of array \u27b\u27, and (3) each distribution pattern matrix of arrays \u27a\u27, \u27b\u27, and \u27c\u27 should have at [east one zero entry, respectively. It is shown that only twelve programs suffice to accomplish redistribution-free execution for the many input data distributions that satisfy the above conditions. When DDI matrix multiplication programs are used in an algorithm with multiple matrix products, half of data redistributions otherwise required can be eliminated

Modular mappings of rectangular algorithms

Affine space-time mappings have been extensively studied for systolic array design and parallelizing compilation. However, there are practical important cases that require other types of transformations. This paper considers so-called modular mappings described by linear transformations modulo a constant vector. Sufficient conditions for these mappings to be one-to-one are investigated for rectangular domains of arbitrary dimensions. It is shown that a sufficient condition for a modular mapping to be one-to-one is that its (n x n) coefficient -matrix T has entries tii = k1 and tij = 0 for i \u3e j where \u3e is a total order on {1, 2,. ., n), n = domain dimension. These conditions are strengthened and extended for particular types of rectangular domains and a.ffine transformations modulo a coinstant vector. The results of this paper can be used to identify a space of valid modular mappings of specific algorithms into time and space. They are illustrated by examples which include Cannon\u27s matrix multiplication algorithm

Toward a Reconfigurable SNMP-based Distributed Monitoring Mechanism for Networked Computing Systems

The dynamic nature of large-size Network Computing Systems (NCSs) and the varying monitoring demands from the end-users pose serious challenges for monitoring systems (MSs). A statically configured MS initially adjusted to perform optimally may end performing poorly. A reconfiguration mechanism for a distributed MS is proposed. It enables the MS to react to changes in the available resources, operating conditions, and monitoring requirements, while maintaining high performance and low monitoring overheads. The distributed MS is organized as a tree, consisting of managed nodes running agents, one or more levels of intermediate-level managers (ILMs), and a top-level manager (TLM) for overall control. A localized decision process involves two adjacent ILM levels. The current values of a local node performance parameter called temperature are used in determining the transformations (merge, split, migrate) for each ILM. The implementation uses SNMP primitives for easy integration in SIMONE, a distributed SNMP-based monitoring system. The interactions between the MS elements and different classes of jobs are studied by defining a queuing model, and by evaluating different configuration schemes using simulation. Results for the static and reconfigurable schemes indicate that reconfiguration improves performance in terms of lower processing delays at the ILMs