64 research outputs found
Efficient tilings of de Bruijn and Kautz graphs
Kautz and de Bruijn graphs have a high degree of connectivity which makes
them ideal candidates for massively parallel computer network topologies. In
order to realize a practical computer architecture based on these graphs, it is
useful to have a means of constructing a large-scale system from smaller,
simpler modules. In this paper we consider the mathematical problem of
uniformly tiling a de Bruijn or Kautz graph. This can be viewed as a
generalization of the graph bisection problem. We focus on the problem of graph
tilings by a set of identical subgraphs. Tiles should contain a maximal number
of internal edges so as to minimize the number of edges connecting distinct
tiles. We find necessary and sufficient conditions for the construction of
tilings. We derive a simple lower bound on the number of edges which must leave
each tile, and construct a class of tilings whose number of edges leaving each
tile agrees asymptotically in form with the lower bound to within a constant
factor. These tilings make possible the construction of large-scale computing
systems based on de Bruijn and Kautz graph topologies.Comment: 29 pages, 11 figure
Sampling cluster endurance for peer-to-peer based content distribution networks
Several types of Content Distribution Networks are being deployed over the Internet today, based on different architectures to meet their requirements (e.g., scalability, efficiency and resiliency). Peer-to-peer (P2P) based Content Distribution Networks are promising approaches that have several advantages. Structured P2P networks, for instance, take a proactive approach and provide efficient routing mechanisms. Nevertheless, their maintenance can increase considerably in highly dynamic P2P environments. In order to address this issue, a two-tier architecture called Omicron that combines a structured overlay network with a clustering mechanism is suggested in a hybrid scheme. In this paper, we examine several sampling algorithms utilized in the aforementioned hybrid network that collect local information in order to apply a selective join procedure. Additionally, we apply the sampling algorithms on Chord in order to evaluate sampling as a general information gathering mechanism. The algorithms are based mostly on random walks inside the overlay networks. The aim of the selective join procedure is to provide a well balanced and stable overlay infrastructure that can easily overcome the unreliable behavior of the autonomous peers that constitute the network. The sampling algorithms are evaluated using simulation experiments as well as probabilistic analysis where several properties related to the graph structure are reveale
Exploiting generalized de-Bruijn/Kautz topologies for flexible iterative channel code decoder architectures
Modern iterative channel code decoder architectures have tight constrains on the throughput but require flexibility to support different modes and standards. Unfortunately, flexibility often comes at the expense of increasing the number of clock cycles required to complete the decoding of a data-frame, thus reducing the sustained throughput. The Network- on-Chip (NoC) paradigm is an interesting option to achieve flexibility, but several design choices, including the topology and the routing algorithm, can affect the decoder throughput. In this work logarithmic diameter topologies, in particular generalized de-Bruijn and Kautz topologies, are addressed as possible solutions to achieve both flexible and high throughput architectures for iterative channel code decoding. In particular, this work shows that the optimal shortest-path routing algorithm for these topologies, that is still available in the open literature, can be efficiently implemented resorting to a very simple circuit. Experimental results show that the proposed architecture features a reduction of about 14% and 10% for area and power consumption respectively, with respect to a previous shortest-path routing-table-based desig
Exploiting generalized de-Bruijn/Kautz topologies for flexible iterative channel code decoder architectures
Modern iterative channel code decoder architectures have tight constrains on the throughput but require flexibility to support different modes and standards. Unfortunately, flexibility often comes at the expense of increasing the number of clock cycles required to complete the decoding of a data-frame, thus reducing the sustained throughput. The Network- on-Chip (NoC) paradigm is an interesting option to achieve flexibility, but several design choices, including the topology and the routing algorithm, can affect the decoder throughput. In this work logarithmic diameter topologies, in particular generalized de-Bruijn and Kautz topologies, are addressed as possible solutions to achieve both flexible and high throughput architectures for iterative channel code decoding. In particular, this work shows that the optimal shortest-path routing algorithm for these topologies, that is still available in the open literature, can be efficiently implemented resorting to a very simple circuit. Experimental results show that the proposed architecture features a reduction of about 14% and 10% for area and power consumption respectively, with respect to a previous shortest-path routing-table-based design
Sampling cluster endurance for peer-to-peer based content distribution networks
Several types of Content Distribution Networks are being deployed over the Internet today, based on different architectures to meet their requirements (e.g., scalability, efficiency and resiliency). Peer-to-peer (P2P) based Content Distribution Networks are promising approaches that have several advantages. Structured P2P networks, for instance, take a proactive approach and provide efficient routing mechanisms. Nevertheless, their maintenance can increase considerably in highly dynamic P2P environments. In order to address this issue, a two-tier architecture called Omicron that combines a structured overlay network with a clustering mechanism is suggested in a hybrid scheme. In this paper, we examine several sampling algorithms utilized in the aforementioned hybrid network that collect local information in order to apply a selective join procedure. Additionally, we apply the sampling algorithms on Chord in order to evaluate sampling as a general information gathering mechanism. The algorithms are based mostly on random walks inside the overlay networks. The aim of the selective join procedure is to provide a well balanced and stable overlay infrastructure that can easily overcome the unreliable behavior of the autonomous peers that constitute the network. The sampling algorithms are evaluated using simulation experiments as well as probabilistic analysis where several properties related to the graph structure are reveale
How Graph Theory can help Communications Engineering
International audienceWe give an overview of different aspects of graph theory which can be applied in communication engineering, not trying to present immediate results to be applied neither a complete survey of results, but to give a flavor of how graph theory can help this field. We deal in this paper with network topologies, resource competition, state transition diagrams and specific models for optical networks
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
Properties and Algorithms of the KCube Graphs
The KCube interconnection topology was rst introduced in 2010. The KCube graph
is a compound graph of a Kautz digraph and hypercubes. Compared with the at-
tractive Kautz digraph and well known hypercube graph, the KCube graph could
accommodate as many nodes as possible for a given indegree (and outdegree) and the diameter of interconnection networks. However, there are few algorithms designed for the KCube graph. In this thesis, we will concentrate on nding graph theoretical properties of the KCube graph and designing parallel algorithms that run on this network. We will explore several topological properties, such as bipartiteness, Hamiltonianicity, and symmetry property. These properties for the KCube graph are very useful to develop efficient algorithms on this network. We will then study the KCube network from the algorithmic point of view, and will give an improved routing algorithm. In addition, we will present two optimal broadcasting algorithms. They are fundamental algorithms to many applications. A literature review of the state of the art network designs in relation to the KCube network as well as some open problems in this field will also be given
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
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