Broadcasting in DMA-bound bounded degree graphs

AbstractBroadcasting is an information dissemination process in which a message is to be sent from a single originator to all members of a network by placing calls over the communication lines of the network. In [2], Bermond, Hell, Liestman and Peters studied the effect, on broadcasting capabilities, of placing an upper bound on the graph's degree. In this paper, we generalize their results allowing calls to involve more than two participants. We give lower bounds and construct bounded degree graphs which allow rapid broadcasting. Our constructions use the nation of compounding graphs in de Bruijin digraphs. We also obtain asymptotic upper and lower bounds for broadcast time, as the maximum degree increases

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

De Bruijn族のグラフの分解及び情報散布への応用に関する研究

学位記番号：工博甲42

Fixed points of Boolean networks, guessing graphs, and coding theory

n this paper, we are interested in the number of fixed points of functions $f:A^n\to A^n$ over a finite alphabet $A$ defined on a given signed digraph $D$. We first use techniques from network coding to derive some lower bounds on the number of fixed points that only depends on $D$. We then discover relationships between the number of fixed points of $f$ and problems in coding theory, especially the design of codes for the asymmetric channel. Using these relationships, we derive upper and lower bounds on the number of fixed points, which significantly improve those given in the literature. We also unveil some interesting behavior of the number of fixed points of functions with a given signed digraph when the alphabet varies. We finally prove that signed digraphs with more (disjoint) positive cycles actually do not necessarily have functions with more fixed points

Properties and Algorithms of the KCube Interconnection Networks

The KCube interconnection network was first introduced in 2010 in order to exploit the good characteristics of two well-known interconnection networks, the hypercube and the Kautz graph. KCube links up multiple processors in a communication network with high density for a fixed degree. Since the KCube network is newly proposed, much study is required to demonstrate its potential properties and algorithms that can be designed to solve parallel computation problems. In this thesis we introduce a new methodology to construct the KCube graph. Also, with regard to this new approach, we will prove its Hamiltonicity in the general KC(m; k). Moreover, we will find its connectivity followed by an optimal broadcasting scheme in which a source node containing a message is to communicate it with all other processors. In addition to KCube networks, we have studied a version of the routing problem in the traditional hypercube, investigating this problem: whether there exists a shortest path in a Qn between two nodes 0n and 1n, when the network is experiencing failed components. We first conditionally discuss this problem when there is a constraint on the number of faulty nodes, and subsequently introduce an algorithm to tackle the problem without restrictions on the number of nodes

Proceedings of the 3rd International Workshop on Optimal Networks Topologies IWONT 2010

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