Showing papers on "De Bruijn graph published in 2000"

Auto-correlation properties of modified de Bruijn sequences

Abstract: Order n de Bruijn (1946) sequences are the period 2/sup n/ binary sequences produced by an n stage feedback shift register. The de Bruijn sequences have good randomness and complexity properties. Auto-correlation functions of modified de Bruijn sequences are examined. Detailed data is presented for orders 4/spl les/n/spl les/6.

Clues to the hidden nature of de Bruijn sequences

Abstract: Order n de Bruijn sequences are the period 2 n binary sequences produced by an n stage feedback shift register. Theoretical results are summarized and data are presented for feedback functions, generator polynomials, linear spans, and autocorrelation properties of modified de Bruijn sequences.

DBG MANs and their routing performance

Abstract: The authors propose the de Bruijn graph (dBG) as a topology for multi-hop lightwave networks and their hierarchical structures. Three routing algorithms that would progressively improve on the mean path length and network throughput-delay performance are studied under various topological variations and locality factors. The study shows that the performance of the bidirectional dBG networks and their hierarchical derivatives are desirable and are comparable to other types of multi-hop systems. Therefore, they are candidates for metropolitan area networks.

De Bruijn isomorphisms and free space optical networks

Abstract: The de Bruijn digraph B(d, D) is usually defined by words of size D on an alphabet of cardinality d, through a cyclic left shift permutation on the words, after which the rightmost symbol is changed. In this paper we show that any digraph defined on words and alphabets of the same size, through an arbitrary permutation on the alphabet and an arbitrary permutation on the word indices, is isomorphic to the de Bruijn, provided that this latter permutation is cyclic. This work is motivated by the next application. It is known that the optical transpose interconnection system from UCSD can implement the de Bruijn interconnections for n nodes, for a fixed d, with O(n) lenses. We show here how to improve this hardware requirement to /spl Theta/(/spl radic/n).

Searching for Spaceships

Abstract: We describe software that searches for spaceships in Conway's Game of Life and related two-dimensional cellular automata. Our program searches through a state space related to the de Bruijn graph of the automaton, using a method that combines features of breadth first and iterative deepening search, and includes fast bit-parallel graph reachability and path enumeration algorithms for finding the successors of each state. Successful results include a new 2c/7 spaceship in Life, found by searching a space with 2^126 states.

Colouring of cycles in the de Bruijn graphs

Abstract: We show that the problem of finding the family of all so called the locally reducible factors in the binary de Bruijn graph of order k is equivalent to the problem of finding all colourings of edges in the binary de Bruijn graph of order k − 1, where each vertex belongs to exactly two cycles of different colours. In this paper we define and study such colouring for the greater class of the de Bruijn graphs in order to define a class of so called regular factors, which is not so difficult to construct. Next we prove that each locally reducible factor of the binary de Bruijn graph is a subgraph of a certain regular factor in the m-ary de Bruijn graph.

A New Multihop Logical Topology for Reliable Broadband Communication

Abstract: This paper presents a new logical topology GIADM-net, a generalised IADM network for enhancing the reliability of optical networks using wavelength division multiplexing. The presence of multiple number of paths of same distance between any two nodes in exchange of reasonable number of hops in the network, ensures a higher degree of reliability compared to other existing topologies in case of link failure, as well as in balancing link loading in the network so as to maximise the network throughput. This GIADM-net, connects any arbitrary no. of nodes in a regular graph as opposed to the cases in De Bruijn graph and shufflenet. The average hopping distance between two nodes, using this topology is smaller, compared to that in GEM net, shufflenet and De Bruijn Graph, at the cost of marginal increase in diameter.