991 research outputs found
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-
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 that are interconnected through a weighted interconnection matrix , where the weight of each inter-graph link is a non-negative real number . Various dynamical processes, such as synchronization, cascading failures
in power grids, and diffusion processes, are described by the Laplacian matrix
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 , being the identity matrix, it has
been shown that there exists a structural transition at some critical coupling,
. This transition is such that dynamical processes are separated into
two regimes: if , the network acts as a whole; whereas when , the network operates as if the graphs encoding the layers were isolated. In
this paper, we extend and generalize the structural transition threshold to a regular interconnection matrix (constant row and column sum).
Specifically, we provide upper and lower bounds for the transition threshold in interdependent networks with a regular interconnection matrix
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 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
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
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
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