Fault-tolerant networks based on the de Bruijn graph

Sridhar, M.A.; Raghavendra, C.S.

doi:10.1109/12.93750

Cited by 39 publications

(14 citation statements)

References 18 publications

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“…Both CAN and Chord are knode-connected 3 , while de Bruijn graphs are not due to several "weak" nodes with self-loops. This classical form of de Bruijn graphs has been shown to be (k−1)-node connected [39]; however, we seek to achieve maximum fault tolerance, which leads us to removing the loops and linking these k "weak" nodes to each other. Consider node (h,h,.…”

Section: Definition 3 a K-regular Graph Is K-node-connected If Therementioning

confidence: 99%

Graph-theoretic analysis of structured peer-to-peer systems: routing distances and fault resilience

Loguinov

Casas²,

Wang

2005

IEEE/ACM Trans. Networking

171

223

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This paper examines graph-theoretic properties of existing peer-to-peer architectures and proposes a new infrastructure based on optimal-diameter de Bruijn graphs. Since generalized de Bruijn graphs possess very short average routing distances and high resilience to node failure, they are well suited for structured peer-to-peer networks. Using the example of Chord, CAN, and de Bruijn, we first study routing performance, graph expansion, and clustering properties of each graph. We then examine bisection width, path overlap, and several other properties that affect routing and resilience of peer-to-peer networks. Having confirmed that de Bruijn graphs offer the best diameter and highest connectivity among the existing peer-to-peer structures, we offer a very simple incremental building process that preserves optimal properties of de Bruijn graphs under uniform user joins/departures. We call the combined peer-to-peer architecture ODRI -Optimal Diameter Routing Infrastructure.

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Section: Definition 3 a K-regular Graph Is K-node-connected If Therementioning

confidence: 99%

Graph-theoretic analysis of structured peer-to-peer systems: routing distances and fault resilience

Loguinov

Casas²,

Wang

2005

IEEE/ACM Trans. Networking

171

223

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“…We therefore need to consider 2-regular graphs leading to fast (classical) mixing and not for example diffusive networks like ring graphs [SS00] FYA84]. De Bruijn graphs have size d k and are equipped with a complete symbolic dynamics of order d. They play an important role in coding theory and parallel algorithms [SR91,SP89]. Numerical evidence suggests that quantum graphs based on de Bruijn digraphs with incommensurate arc lengths follow random matrix statistics in the limit of large graphs sizes even for d = 2 [Ta00,Ta01].…”

Section: Regular De Bruijn Quantum Graphsmentioning

confidence: 99%

Regular quantum graphs

Severini

Tanner

2004

J. Phys. A: Math. Gen.

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We introduce the concept of regular quantum graphs and construct connected quantum graphs with discrete symmetries. The method is based on a decomposition of the quantum propagator in terms of permutation matrices which control the way incoming and outgoing channels at vertex scattering processes are connected. Symmetry properties of the quantum graph as well as its spectral statistics depend on the particular choice of permutation matrices, also called connectivity matrices, and can now be easily controlled. The method may find applications in the study of quantum random walks networks and may also prove to be useful in analysing universality in spectral statistics.

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“…There are constructions for de Bruijn sequences for arbitrary c and u in [5], [9], [23], [25], [26]. The de Bruijn graph has received much attention in the literature: [9] provides a good survey, while applications have been proposed for the de Bruijn graph and de Bruijn sequences in the fields of communications and coding, [4], [11], [24], position sensing, [1], and in Cryptography, [12].…”

Section: Definition a T-cycle Inmentioning

confidence: 99%

Perfect factors in the de Bruijn graph

Paterson

1995

Des Codes Crypt

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Abstract.A Perfect Factor in the de Bruijn graph is a collection of disjoint cycles of a fixed period with the property that each vertex of the graph lies on exactly one cycle. Alternatively a Perfect Factor is a set of periodic sequences of a fixed period such that for some fixed u, every possible u-tuple of consecutive symbols occurs exactly once as a sub-sequence of a sequence of the set. As well as being of interest in their own right, Perfect Factors are fundamental in the construction of Perfect Maps in two dimensions. In this paper, necessary conditions on the period for the existence of Perfect Factors are given. These conditions are shown to be sufficient in the case where the size of the alphabet is a power of a prime. We also consider the construction of Perfect Factors over general c-ary alphabets. Our results are then applied to obtain a large new class of non-binary Perfect Maps.

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Fault-tolerant networks based on the de Bruijn graph

Cited by 39 publications

References 18 publications

Graph-theoretic analysis of structured peer-to-peer systems: routing distances and fault resilience

Graph-theoretic analysis of structured peer-to-peer systems: routing distances and fault resilience

Regular quantum graphs

Perfect factors in the de Bruijn graph

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