97 research outputs found

    Broadcasting in DMA-bound bounded degree graphs

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    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

    Rates of DNA Sequence Profiles for Practical Values of Read Lengths

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    A recent study by one of the authors has demonstrated the importance of profile vectors in DNA-based data storage. We provide exact values and lower bounds on the number of profile vectors for finite values of alphabet size qq, read length ℓ\ell, and word length nn.Consequently, we demonstrate that for q≥2q\ge 2 and n≤qℓ/2−1n\le q^{\ell/2-1}, the number of profile vectors is at least qκnq^{\kappa n} with κ\kappa very close to one.In addition to enumeration results, we provide a set of efficient encoding and decoding algorithms for each of two particular families of profile vectors

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

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

    Bus interconnection networks

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    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

    Master index: volumes 31–40

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