A systematic analysis of equivalence in multistage networks

Many approaches to switching in optoelectronic and optical networks decompose the switching function across multiple stages or hops. This paper addresses the problem of determining whether two multistage or multihop networks are functionally equivalent. Various ad-hoc methods have been used in the past to establish such equivalences. A systematic method for determining equivalence is presented based on properties of the link permutations used to interconnect stages of the network. This method is useful in laying out multistage networks, in determining optimal channel assignments for multihop networks, and in establishing the routing required in such networks. A purely graphical variant of the method, requiring no mathematics or calculations, is also described

Modeling of Topologies of Interconnection Networks based on Multidimensional Multiplicity

Modern SoCs are becoming more complex with the integration of heterogeneous components (IPs). For this purpose, a high performance interconnection medium is required to handle the complexity. Hence NoCs come into play enabling the integration of more IPs into the SoC with increased performance. These NoCs are based on the concept of Interconnection networks used to connect parallel machines. In response to the MARTE RFP of the OMG, a notation of multidimensional multiplicity has been proposed which permits to model repetitive structures and topologies. This report presents a modeling methodology based on this notation that can be used to model a family of Interconnection Networks called Delta Networks which in turn can be used for the construction of NoCs

A Frame Work for Parallel String Matching- A Computational Approach with Omega Model

Now a day2019;s parallel string matching problem is attracted by so many researchers because of the importance in information retrieval systems. While it is very easily stated and many of the simple algorithms perform very well in practice, numerous works have been published on the subject and research is still very active. In this paper we propose a omega parallel computing model for parallel string matching. Experimental results show that, on a multi-processor system, the omega model implementation of the proposed parallel string matching algorithm can reduce string matching time by more than 40%

Testing Layered Interconnection Networks

We present an approach for fault detection in layered interconnection networks (LINs). An LIN is a generalized multistage interconnection network commonly used in reconfigurable systems; the nets (links) are arranged in sets (referred to as layers) of different size. Switching elements (made of simple switches such as transmission-gate-like devices) are arranged in a cascade to connect pairs of layers. The switching elements of an LIN have the same number of switches, but the switching patterns may not be uniform. A comprehensive fault model for the nets and switches is assumed at physical and behavioral levels. Testing requires configuring the LIN multiple times. Using a graph approach, it is proven that the minimal set of configurations corresponds to the node disjoint path sets. The proposed approach is based on two novel results in the execution of the network flow algorithm to find node disjoint path sets, while retaining optimality in the number of configurations. These objectives are accomplished by finding a feasible flow such that the maximal degree can be iteratively decreased, while guaranteeing the existence of an appropriate circulation. Net adjacencies are also tested for possible bridge faults (shorts). To account for 100 percent fault coverage of bridge faults a postprocessing algorithm may be required; bounds on its complexity are provided. The execution complexity of the proposed approach (inclusive of test vector generation and post-processing) is O(N4WL), where N is the total number of nets, W is the number of switches per switching element, and L is the number of layers. Extensive simulation results are provided

Reconfiguration for Fault Tolerance and Performance Analysis

Architecture reconfiguration, the ability of a system to alter the active interconnection among modules, has a history of different purposes and strategies. Its purposes develop from the relatively simple desire to formalize procedures that all processes have in common to reconfiguration for the improvement of fault-tolerance, to reconfiguration for performance enhancement, either through the simple maximizing of system use or by sophisticated notions of wedding topology to the specific needs of a given process. Strategies range from straightforward redundancy by means of an identical backup system to intricate structures employing multistage interconnection networks. The present discussion surveys the more important contributions to developments in reconfigurable architecture. The strategy here is in a sense to approach the field from an historical perspective, with the goal of developing a more coherent theory of reconfiguration. First, the Turing and von Neumann machines are discussed from the perspective of system reconfiguration, and it is seen that this early important theoretical work contains little that anticipates reconfiguration. Then some early developments in reconfiguration are analyzed, including the work of Estrin and associates on the fixed plus variable restructurable computer system, the attempt to theorize about configurable computers by Miller and Cocke, and the work of Reddi and Feustel on their restructable computer system. The discussion then focuses on the most sustained systems for fault tolerance and performance enhancement that have been proposed. An attempt will be made to define fault tolerance and to investigate some of the strategies used to achieve it. By investigating four different systems, the Tandern computer, the C.vmp system, the Extra Stage Cube, and the Gamma network, the move from dynamic redundancy to reconfiguration is observed. Then reconfiguration for performance enhancement is discussed. A survey of some proposals is attempted, then the discussion focuses on the most sustained systems that have been proposed: PASM, the DC architecture, the Star local network, and the NYU Ultracomputer. The discussion is organized around a comparison of control, scheduling, communication, and network topology. Finally, comparisons are drawn between fault tolerance and performance enhancement, in order to clarify the notion of reconfiguration and to reveal the common ground of fault tolerance and performance enhancement as well as the areas in which they diverge. An attempt is made in the conclusion to derive from this survey and analysis some observations on the nature of reconfiguration, as well as some remarks on necessary further areas of research

Symmetric rearrangeable networks and algorithms

A class of symmetric rearrangeable nonblocking networks has been considered in this thesis. A particular focus of this thesis is on Benes networks built with 2 x 2 switching elements. Symmetric rearrangeable networks built with larger switching elements have also being considered. New applications of these networks are found in the areas of System on Chip (SoC) and Network on Chip (NoC). Deterministic routing algorithms used in NoC applications suffer low scalability and slow execution time. On the other hand, faster algorithms are blocking and thus limit throughput. This will be an acceptable trade-off for many applications where achieving ”wire speed” on the on-chip network would require extensive optimisation of the attached devices. In this thesis I designed an algorithm that has much lower blocking probabilities than other suboptimal algorithms but a much faster execution time than deterministic routing algorithms. The suboptimal method uses the looping algorithm in its outermost stages and then in the two distinct subnetworks deeper in the switch uses a fast but suboptimal path search method to find available paths. The worst case time complexity of this new routing method is O(NlogN) using a single processor, which matches the best known results reported in the literature. Disruption of the ongoing communications in this class of networks during rearrangements is an open issue. In this thesis I explored a modification of the topology of these networks which gives rise to what is termed as repackable networks. A repackable topology allows rearrangements of paths without intermittently losing connectivity by breaking the existing communication paths momentarily. The repackable network structure proposed in this thesis is efficient in its use of hardware when compared to other proposals in the literature. As most of the deterministic algorithms designed for Benes networks implement a permutation of all inputs to find the routing tags for the requested inputoutput pairs, I proposed a new algorithm that can work for partial permutations. If the network load is defined as ρ, the mean number of active inputs in a partial permutation is, m = ρN, where N is the network size. This new method is based on mapping the network stages into a set of sub-matrices and then determines the routing tags for each pair of requests by populating the cells of the sub-matrices without creating a blocking state. Overall the serial time complexity of this method is O(NlogN) and O(mlogN) where all N inputs are active and with m < N active inputs respectively. With minor modification to the serial algorithm this method can be made to work in the parallel domain. The time complexity of this routing algorithm in a parallel machine with N completely connected processors is O(log^2 N). With m active requests the time complexity goes down to (logmlogN), which is better than the O(log^2 m + logN), reported in the literature for 2^0.5((log^2 -4logN)^0.5-logN)<= ρ <= 1. I also designed multistage symmetric rearrangeable networks using larger switching elements and implement a new routing algorithm for these classes of networks. The network topology and routing algorithms presented in this thesis should allow large scale networks of modest cost, with low setup times and moderate blocking rates, to be constructed. Such switching networks will be required to meet the bandwidth requirements of future communication networks