Tolerating multiple faults in multistage interconnection networks with minimal extra stages

Adams and Siegel (1982) proposed an extra stage cube interconnection network that tolerates one switch failure with one extra stage. We extend their results and discover a class of extra stage interconnection networks that tolerate multiple switch failures with a minimal number of extra stages. Adopting the same fault model as Adams and Siegel, the faulty switches can be bypassed by a pair of demultiplexer/multiplexer combinations. It is easy to show that, to maintain point to point and broadcast connectivities, there must be at least S extra stages to tolerate I switch failures. We present the first known construction of an extra stage interconnection network that meets this lower-bound. This 12-dimensional multistage interconnection network has n+f stages and tolerates I switch failures. An n-bit label called mask is used for each stage that indicates the bit differences between the two inputs coming into a common switch. We designed the fault-tolerant construction such that it repeatedly uses the singleton basis of the n-dimensional vector space as the stage mask vectors. This construction is further generalized and we prove that an n-dimensional multistage interconnection network is optimally fault-tolerant if and only if the mask vectors of every n consecutive stages span the n-dimensional vector space

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

Optical Interconnection Networks Based on Microring Resonators

Abstract — Interconnection networks must transport an always increasing information density and connect a rising number of processing units. Electronic technologies have been able to sustain the traffic growth rate, but are getting close to their physical limits. In this context, optical interconnection networks are becoming progressively more attractive, especially because new photonic devices can be directly integrated in CMOS technology. Indeed, interest in microring resonators as switching components is rising, but their usability in full optical interconnection architectures is still limited by their physical characteristics. Indeed, differently from classical devices used for switching, switching elements based on microring resonators exhibit asymmetric power losses depending on the output ports input signals are directed to. In this paper, we study classical interconnection architectures such as crossbar, Benes and Clos networks exploiting microring resonators as building blocks. Since classical interconnection networks lack either scalability or complexity, we propose two new architectures to improve performance of microring based interconnection networks while keeping a reasonable complexity. I

A challenge for routing algorithms in optical multistage interconnection networks

Problem statement: A class of dynamic interconnection networks is Multistage Interconnection Networks (MINs) that connects input devices to output devices through a number of switch stages. MINs have assumed importance in recent years; because of their cost-effectiveness. Optical MINs are one type of MINs that have large transmission capacity in the communication networks. There is a major problem in Optical MIN that is crosstalk, which is caused by coupling two signals within a switching element. Approach: To avoid crosstalk in Optical MINs many algorithms have been proposed by many researchers that we review applying five routing algorithms and scheduling them in the Optical MINs. Results: The comparative results of routing algorithms show affective of avoiding crosstalk in number of passes and execution time for different algorithm. Conclusion: The challenge between these routing algorithms is thoroughly investigated, by applying them on Optical MIN and showing which algorithm has better performance to avoid crosstalk

Expanded delta networks for very large parallel computers

In this paper we analyze a generalization of the traditional delta network, introduced by Patel [21], and dubbed Expanded Delta Network (EDN). These networks provide in general multiple paths that can be exploited to reduce contention in the network resulting in increased performance. The crossbar and traditional delta networks are limiting cases of this class of networks. However, the delta network does not provide the multiple paths that the more general expanded delta networks provide, and crossbars are to costly to use for large networks. The EDNs are analyzed with respect to their routing capabilities in the MIMD and SIMD models of computation.The concepts of capacity and clustering are also addressed. In massively parallel SIMD computers, it is the trend to put a larger number processors on a chip, but due to I/O constraints only a subset of the total number of processors may have access to the network. This is introduced as a Restricted Access Expanded Delta Network of which the MasPar MP-1 router network is an example

Shortest paths in orthogonal graphs

Orthogonal graphs were introduced as a simple but powerful tool for the description and analysis of a class of interconnection networks. Routing, and hence finding shortest paths between any two nodes of an orthogonal graph, becomes an important problem. It is shown in this paper that routing in this class of graphs reduces to a node covering problem in the bipartite coverage graph of the orthogonal graph. A minimum cover clearly leads to a shortest path. In general, the problem of finding the mínimum node cover in a bipartite graph is NP-complete. However, the bipartite coverage graphs corresponding to orthogonal graphs have a regular pattern of edges. This allows the development of a routing algorithm which results in a minimum cover. The procedure executes in polynomial time in the number of bit-nodes of the bipartite graph. It therefore results in a shortest path algorithm whose time complexity is quadratic in the logarithm of the number of nodes in the original orthogonal graph