Showing papers on "De Bruijn graph published in 2004"

Tiling the ( n 2 , 1)-De Bruijn Graph with n Coassociative Coalgebras

Abstract: We construct, via usual graph theory a class of associative dialgebras as well as a class of coassociative L-coalgebras, the two classes being related by a tool from graph theory called the line-extension. As a corollary, a tiling of the n 2-De Bruijn graph with n (geometric supports of) coassociative coalgebras is obtained. Via the tiling of the (3, 1)-De Bruijn graph, we also get an example of cubical trialgebra, notion introduced by Loday and Ronco. Other examples are obtained by letting M n (k) act on axioms defining such tilings. Examples of associative products which split into several associative ones are also given.

De Bruijn cycles for covering codes

Abstract: A de Bruijn covering code is a q-ary string S so that every q-ary string is at most R symbol changes from some n-word appearing consecutively in S. We introduce these codes and prove that they can have size close to the smallest possible covering code. The proof employs tools from field theory, probability, and linear algebra. Included is a table of the best known bounds on the lengths of small binary de Bruijn covering codes, up to R = 11 and n = 13, followed by several open questions in this area. © 2004 Wiley Periodicals, Inc. Random Struct. Alg., 2004

Minimal de bruijn sequence in a language with forbidden substrings

Abstract: Let be the following strategy to construct a walk in a labeled digraph: at each vertex, we follow the unvisited arc of minimum label. In this work we study for which languages, applying the previous strategy over the corresponding de Bruijn graph, we finish with an Eulerian cycle, in order to obtain the minimal de Bruijn sequence of the language.

Efficient routing and broadcasting algorithms in de bruijn networks

Abstract: Recently, routing on dBG has been investigated as shortest path and fault tolerant routing but investigation into shortest path in failure mode on dBG has been non-existent. Furthermore, dBG based broadcasting has been studied as local broadcasting and arc-disjoint spanning trees based broadcasting. However, their broadcasting algorithms can only work in dBG(2,k). In this paper, we investigate shortest path routing algorithms in the condition of existing failure, based on the Bidirectional de Bruijn graph (BdBG). And we also investigate broadcasting in BdBG for a degree greater than or equal to two.

Implementation and evaluation of Shufflenet, Gemnet and De Bruijn graph logical network topologies

Abstract: In this paper, a generic model for implementing logical interconnection topologies in software has been proposed in order to investigate the performance of the logical topologies and their routing algorithms for packet based synchronous networks. This model is generic for synchronous transfer modes and therefore can be used in implementing any logical topology by using any programming language. Three topologies have been investigated and implemented namely: Shufflenet, De Bruijn graph and Gemnet. Results for the average packet delay show that the De Bruijn graph performed the worst. Also, it is observed that the De Bruijn graph makes use of buffering more efficiently compared to the other algorithms.

Minimal de Bruijn sequence in a language with forbidden substrings

Abstract: Let be the following strategy to construct a walk in a labeled digraph: at each vertex, we follow the unvisited arc of minimum label. In this work we study for which languages, applying the previous strategy over the corresponding de Bruijn graph, we finish with an Eulerian cycle, in order to obtain the minimal de Bruijn sequence of the language.

Super edge-connectivity of de bruijn and kautz undirected graphs

Abstract: The super edge-connectivity of a graph is an important parameter to measure fault-tolerance of interconnection networks. This note shows that the Kautz undirected graph is super edge-connected,and provides a short proof of Lue and Zhang's result on super edge-connectivity of the de Bruijn undirected graph.

Improved bounds on cutwidths of shuffle-exchange and de bruijn graphs

Abstract: We prove that the cutwidth of the n-dimensional shuffle-exchange graph is at most ⌈2n+1/n⌉, for n≥10 This essentially improves on the previous best constant factors As a consequence we obtain an improved upper bound for the cutwidth of the de Bruijn graph

Topology aggregation schemes for asymmetric link state information

Abstract: In this paper, we present two algorithms for efficiently aggregating link state information needed for quality-of-service (QoS) routing. In these algorithms, each edge node in a group is mapped onto a node of a shufflenet or a node of a de Bruijn graph. By this mapping, the number of links for which state information is maintained becomes aN (a is an integer, N is the number of edge nodes) which is significantly smaller than N2 in the full-mesh approach. Our algorithms also can support asymmetric link state parameters which are common in practice, while many previous algorithms such as the spanning tree approach can be applied only to networks with symmetric link state parameters. Experimental results show that the performance of our shufflenet algorithm is close to that of the full-mesh approach in terms of the accuracy of bandwidth and delay information, with only a much smaller amount of information. On the other hand, although it is not as good as the shufflenet approach, the de Bruijn algorithm also performs far better than the star approach which is one of the most widely accepted schemes. The de Bruijn algorithm needs smaller computational complexity than most previous algorithms for asymmetric networks, including the shufflenet algorithm.

An optimal broadcasting algorithm for de bruijn network dBG(d,k)

Abstract: Recent works have classified de Bruijn graph (dBG) based broadcasting algorithms into local broadcasting and arc-disjoint spanning trees based broadcasting. However, those algorithms can only work in binary dBG. In this paper, we investigate broadcasting in bidirectional dBG for a degree greater than or equal to two. A distributed broadcast algorithm for one-to-all broadcasting in the all port communication is proposed for dBG(d,k).

Unicontour Isomorphic Factorizations of de Bruijn and Kautz Digraphs

Abstract: In the topology of information networks, problems arise of existence and implementation of a decomposition of some network into factor-graphs that have no common edges and to which certain specified features are assigned. Special attention is given to isomorphic expansions and factorizations of graphs in the case where obtained components are simplest topologic network structures. The factorized character of Bruijn and Kautz graphs on a set of specific families of unicontour oriented factors is proved.