Bus interconnection networks

AbstractIn bus interconnection networks every bus provides a communication medium between a set of processors. These networks are modeled by hypergraphs where vertices represent the processors and edges represent the buses. We survey the results obtained on the construction methods that connect a large number of processors in a bus network with given maximum processor degree Δ, maximum bus size r, and network diameter D. (In hypergraph terminology this problem is known as the (Δ,D, r)-hypergraph problem.)The problem for point-to-point networks (the case r = 2) has been extensively studied in the literature. As a result, several families of networks have been proposed. Some of these point-to-point networks can be used in the construction of bus networks. One approach is to consider the dual of the network. We survey some families of bus networks obtained in this manner. Another approach is to view the point-to-point networks as a special case of the bus networks and to generalize the known constructions to bus networks. We provide a summary of the tools developed in the theory of hypergraphs and directed hypergraphs to handle this approach

Reduction of Second-Order Network Systems with Structure Preservation

This paper proposes a general framework for structure-preserving model reduction of a secondorder network system based on graph clustering. In this approach, vertex dynamics are captured by the transfer functions from inputs to individual states, and the dissimilarities of vertices are quantified by the H2-norms of the transfer function discrepancies. A greedy hierarchical clustering algorithm is proposed to place those vertices with similar dynamics into same clusters. Then, the reduced-order model is generated by the Petrov-Galerkin method, where the projection is formed by the characteristic matrix of the resulting network clustering. It is shown that the simplified system preserves an interconnection structure, i.e., it can be again interpreted as a second-order system evolving over a reduced graph. Furthermore, this paper generalizes the definition of network controllability Gramian to second-order network systems. Based on it, we develop an efficient method to compute H2-norms and derive the approximation error between the full-order and reduced-order models. Finally, the approach is illustrated by the example of a small-world network

A Design Methodology for Space-Time Adapter

This paper presents a solution to efficiently explore the design space of communication adapters. In most digital signal processing (DSP) applications, the overall architecture of the system is significantly affected by communication architecture, so the designers need specifically optimized adapters. By explicitly modeling these communications within an effective graph-theoretic model and analysis framework, we automatically generate an optimized architecture, named Space-Time AdapteR (STAR). Our design flow inputs a C description of Input/Output data scheduling, and user requirements (throughput, latency, parallelism...), and formalizes communication constraints through a Resource Constraints Graph (RCG). The RCG properties enable an efficient architecture space exploration in order to synthesize a STAR component. The proposed approach has been tested to design an industrial data mixing block example: an Ultra-Wideband interleaver.Comment: ISBN : 978-1-59593-606-

Algebraic and Computer-based Methods in the Undirected Degree/diameter Problem - a Brief Survey

This paper discusses the most popular algebraic techniques and computational methods that have been used to construct large graphs with given degree and diameter

Structural transition in interdependent networks with regular interconnections

Networks are often made up of several layers that exhibit diverse degrees of interdependencies. A multilayer interdependent network consists of a set of graphs $G$ that are interconnected through a weighted interconnection matrix $B$, where the weight of each inter-graph link is a non-negative real number $p$. Various dynamical processes, such as synchronization, cascading failures in power grids, and diffusion processes, are described by the Laplacian matrix $Q$ characterizing the whole system. For the case in which the multilayer graph is a multiplex, where the number of nodes in each layer is the same and the interconnection matrix $B=pI$, being $I$ the identity matrix, it has been shown that there exists a structural transition at some critical coupling, $p^*$. This transition is such that dynamical processes are separated into two regimes: if $p > p^*$, the network acts as a whole; whereas when $p<p^*$, the network operates as if the graphs encoding the layers were isolated. In this paper, we extend and generalize the structural transition threshold $p^*$ to a regular interconnection matrix $B$ (constant row and column sum). Specifically, we provide upper and lower bounds for the transition threshold $p^*$ in interdependent networks with a regular interconnection matrix $B$ and derive the exact transition threshold for special scenarios using the formalism of quotient graphs. Additionally, we discuss the physical meaning of the transition threshold $p^*$ in terms of the minimum cut and show, through a counter-example, that the structural transition does not always exist. Our results are one step forward on the characterization of more realistic multilayer networks and might be relevant for systems that deviate from the topological constrains imposed by multiplex networks.Comment: 13 pages, APS format. Submitted for publicatio

Model Reduction Methods for Complex Network Systems

Network systems consist of subsystems and their interconnections, and provide a powerful framework for analysis, modeling and control of complex systems. However, subsystems may have high-dimensional dynamics, and the amount and nature of interconnections may also be of high complexity. Therefore, it is relevant to study reduction methods for network systems. An overview on reduction methods for both the topological (interconnection) structure of the network and the dynamics of the nodes, while preserving structural properties of the network, and taking a control systems perspective, is provided. First topological complexity reduction methods based on graph clustering and aggregation are reviewed, producing a reduced-order network model. Second, reduction of the nodal dynamics is considered by using extensions of classical methods, while preserving the stability and synchronization properties. Finally, a structure-preserving generalized balancing method for simplifying simultaneously the topological structure and the order of the nodal dynamics is treated.Comment: To be published in Annual Review of Control, Robotics, and Autonomous System