De Bruijn Networks Research Articles

A Distributed Cloud Architecture Based on General De Bruijn Overlay Network

Distributed cloud systems enable the distribution of computing resources across various geographical locations. While offering benefits like accelerated content delivery, the scalability and coherence maintenance of these systems pose significant challenges. Recent studies reveal shortcomings in existing distributed system schemes to meet modern cloud application demands and maintain coherence among heterogeneous system elements. This paper proposes a service-oriented network architecture for distributed cloud computing networks. Using a De Bruijn network as a software-defined overlay network, the architecture ensures scalability and coherence. Through service-based addressing, requests are issued to designated service address bands, streamlining service discovery. The architecture's evaluation through extensive simulations showcases sustainable scalability and inherent load-balancing properties. The paper concludes with insights into future research directions, emphasizing the extension of the proposed architecture to emerging distributed cloud use cases and decentralized security.

A parallel algorithm for motion estimation in video coding using the bilinear transformation.

Accurate motion estimation between frames is important for drastically reducing data redundancy in video coding. However, advanced motion estimation methods are computationally intensive and their execution in real time usually requires a parallel implementation. In this paper, we investigate the parallel implementation of such a motion estimation technique. Specifically, we present a parallel algorithm for motion estimation based on the bilinear transformation on the well-known parallel model of the hypercube network and formally prove the time and the space complexity of the proposed algorithm. We also show that the parallel algorithm can also run on other hypercubic networks, such as butterfly, cube-connected-cycles, shuffle-exchange or de Bruijn network with only constant slowdown.

Choosing a heuristic and root node for edge ordering in BDD-based network reliability analysis

In the Binary Decision Diagram (BDD)-based network reliability analysis, heuristics have been widely used to obtain a reasonably good ordering of edge variables. Orderings generated using different heuristics can lead to dramatically different sizes of BDDs, and thus dramatically different running times and memory usages for the analysis of the same network. Unfortunately, due to the nature of the ordering problem (i.e., being an NP-complete problem) no formal guidelines or rules are available for choosing a good heuristic or for choosing a high-performance root node to perform edge searching using a particular heuristic. In this work, we make novel contributions by proposing heuristic and root node selection methods based on the concept of boundary sets for the BDD-based network reliability analysis. Empirical studies show that the proposed selection methods can help to generate high-performance edge ordering for most of studied cases, enabling the efficient BDD-based reliability analysis of large-scale networks. The proposed methods are demonstrated on different types of networks, including square lattice networks, torus lattice networks and de Bruijn networks.

New insights into breadth-first search edge ordering of regular networks for terminal-pair reliability analysis

In the binary decision diagram–based terminal-pair network reliability analysis, the size of binary decision diagram heavily depends on the chosen edge ordering. From a theoretical point of view, finding the best ordering is an intractable task. Therefore, heuristics have been used to obtain reasonably good orderings. Among them, the breadth-first search heuristic typically outperforms other heuristics by generating smaller binary decision diagram and thus has been widely used for terminal-pair network reliability analysis. However, the performance of breadth-first search is still only vaguely understood; not much formal work has been done. In this work, we investigate the selection of high-performance root node of breadth-first search ordering for both lattice networks and de Bruijn networks. Empirical study shows that using the two terminal nodes in the terminal-pair network reliability analysis as the root node of the breadth-first search heuristic can have poor performance, and the high-performance root nodes are not randomly distributed. The relationship between the distribution pattern of high-performance root nodes and the rearrangement of successors is also studied. Given that there is often a variation of several orders of magnitude between the sizes of binary decision diagram built using different root nodes for the same network, the application of our results can dramatically reduce the running time and memory usage and make the binary decision diagram–based reliability analysis of large-scale regular networks possible.

The [formula omitted]-tuple twin domination in generalized de Bruijn and Kautz networks

Given a digraph (network) G = ( V , A ) , a vertex u in G is said to out-dominate itself and all vertices v such that the arc ( u , v ) ∈ A ; similarly, u in-dominates both itself and all vertices w such that the arc ( w , u ) ∈ A . A set D of vertices of G is a k - tuple twin dominating set if every vertex of G is out-dominated and in-dominated by at least k vertices in D , respectively. The k -tuple twin domination problem is to determine a minimum k -tuple twin dominating set for a digraph. In this paper we investigate the k -tuple twin domination problem in generalized de Bruijn networks G B ( n , d ) and generalized Kautz G K ( n , d ) networks when d divides n . We provide construction methods for constructing minimum k -tuple twin dominating sets in these networks. These results generalize previous results given by Araki [T. Araki, The k -tuple twin domination in de Bruijn and Kautz digraphs, Discrete Mathematics 308 (2008) 6406–6413] for de Bruijn and Kautz networks.

A wavelength assignment algorithm for de Bruijn WDM networks

This paper proposes an offline wavelength assignment technique for de Bruijn (d, k) optical wavelength division multiplexing (WDM) networks having nodal degree d and diameter k that can support lightpaths between pair of nodes. Each lightpath uses a channel (wavelength) along each link in its route. An efficient algorithm is proposed that can be used to assign wavelengths to lightpath requests in O(k|V|) time, where |V| represents the number of nodes of the de Bruijn network and V represents the set of nodes. The proposed algorithm can be efficiently used for wavelength assignment in de Bruijn WDM networks having limited wavelength conversion capabilities. This work shows that de Bruijn graph can be expressed as union of edge-disjoint rings. Wavelengths are assigned for the individual rings in the graph thus resulting in the assignment for the graph itself. Results are shown for a given de Bruijn graph and for an arbitrary request. The proposed algorithm is compared with two other algorithms, which use two other known works of wavelength assignment on ring topology. Comparisons of the time complexity and the type of wavelength conversion required for these algorithms clearly show that the proposed algorithm is a faster and more efficient way of assigning wavelengths.

Spanning Trees for Binary Directed DE Bruijn Networks and Their Applications to Load Balancing

One of the major reasons of using parallel computer systems is that they have the potential for improving performance and resource sharing. To achieve this, an efficient way must be provided to broadcast a message or messages from a node to every other nodes in the system. However, the efficiency of transferring messages in a system is determined by the architecture of the underlying inter connection network of the system. In this paper, we consider the systems based on binary directed de Bruijn networks and define two shortest path spanning trees: the upward-0 spanning tree and the downward-0spanning tree, to meet various message transfer requirements. To demonstrate the usage of these spanning trees, an application to the load-balancing problem is considered. The resulting time complexity is O(log＾(2)N+Σ(subscript 〓△i≠0)△(subscript i)),where N is the number of nodes and△(subscript i)is the total transfer time for the load difference of each node i, for all 1≤i≤N,on the binary directed de Bruijn networks.

Parallel algorithm for matrix multiplication based on De Bruijn network

It is necessary to develop parallel matrix multiplication because of serial matrix multiplication costing much memory and time.Many different parallel matrix multiplications have been developed according to different network topologies.De Bruijn network is one of the most attractive network models,which has good parallel computing performance.It is simple to execute parallel matrix multiplication on De Bruijn network and easy to implement.In this paper,De Bruijn network was introduced,and then a parallel algorithm for matrix multiplication based on De Bruijn network was proposed.Its speedup ratio,efficiency and scalability were analyzed.It is proved by experiments and comparison that this algorithm is equal to Cannon's in terms of time complexity.

The Independence Number for De Bruijn networks and Kautz networks

Let D be a directed graph; the (l,ω)-Independence Number of graph D, denoted by αl,ω(D), is an important performance parameter for interconnection networks. De Bruijn networks and Kautz networks, denoted by B(d,n) and K(d,n) respectively, are versatile and efficient topological structures of interconnection networks. For l=1,2,…,n, this paper shows that αl,d−1(B(d,n))=dn,αl,d−1(K(d,n))=αl,d(K(d,n))=dn+dn−1 if d≥3 and n≤d−2. In particular, the paper shows the exact value of the Independence Number for B(d,1) and B(d,2) for any d. For the generalized situation, the paper obtains a lower bound αl,d−1(B(d,n))≥d2 if n≥3 and d≥5.

A Note on the Implementation of de Bruijn Networks by the Optical Transpose Interconnection System

This note shows an efficient implementation of de Bruijn networks by the Optical Transpose Interconnection System (OTIS) extending previous results by Coudert, Ferreira, and Perennes [2].

Some mathematical properties of cayley digraphs with applications to interconnection network design

We consider the relationships between Cayley digraphs and their coset graphs with respect to subgroups and obtain some general results on homomorphism and broadcasting between them. We also derive a general factorization theorem on subgraphs of Cayley digraphs by their automorphism groups. We discuss the applications of these results to well-known interconnection networks such as the butterfly network, the de Bruijn network, the cube-connected cycles network and the shuffle-exchange network.

Randomized routing and wavelength requirements in wavelength-routed WDM multistage, hypercube, and de Bruijn networks

This paper considers randomized routing in wavelength-routed wavelength division multiplexed (WDM) networks. Randomized routing is advantageous when compared to deterministic routing, as it is simple, oblivious, and suitable for centralized as well as distributed implementation. Recently, there has been a considerable interest in studying regular graphs such as shuffle networks and de Bruijn networks as a possible physical topology for wavelength-routed WDM networks (IEEE/ACM Trans. Network 3(3) (June 1995) 269; IEEE/ACM Trans. Network 2(1) (February 1994) 70; Comput. Networks ISDN Systems 30(24) (December 1998) 2349). In Pankaj and Gallager (1995), permutation routing has been taken as a benchmark problem to accept a network and a deterministic algorithm has been proposed for routing permutation traffic without any blocking in an N-node wrapped-around multi-stage shuffle network using O( log 3 N) wavelengths. In this paper, we look at the possible application of probabilistic techniques on a class of wrapped-around multi-stage networks called 2-multinets and study the wavelength requirements for routing permutation traffic, allowing a negligible blocking of sessions. We adopt the routing scheme proposed in (J. ACM 31 (1984) 507) for fast packet routing to find routes in the circuit-switched wavelength-routed WDM networks and analyze the wavelength requirements for different models. The models differ in their routing node architecture and wavelength selection policy. Our analysis shows that the permutation routing problem can be solved on these models with an overwhelming probability using O( log 2 N) wavelengths. We also study the routing problem on 2-multinets for a class of 1-expectedly bounded connection requests. For this class also, we propose two models and obtain similar bounds on the number of wavelengths required. We confirm the theoretical results by extensive simulation experiments. The theoretical as well as experimental results show that the number of wavelengths required is reduced significantly when randomized routing techniques are used. Finally, we discuss how the results obtained for 2-multinets can be extended to hypercubes and de Bruijn networks.

EFFICIENT ALGORITHMS FOR SELECTION AND SORTING OF LARGE DISTRIBUTED FILES ON DE BRUIJN AND HYPERCUBE STRUCTURES

In this paper we show the power of sampling techniques in designing efficient distributed algorithms. In particular, we apply sampling techniques in the design of selection algorithms on the hypercube and de Bruijn networks, and show that the message complexity of selecting an item from a set (file) is less sensitive to the cardinality of the set (file). Given a file with n keys, our algorithm performs a selection on a p-node de Bruijn network or hypercube using only O(p log log n) messages and suffering a delay of O(τ log p log log n), with high probability. Our selection scheme outperforms the existing approaches in terms of both message complexity and communication delay. Because of the lesser sensitivity of message complexity and communication delay of our algorithms to the file size, our distributed selection schemes are very attractive in applications where very large database systems are involved. Using our selection algorithms, we also show that both quicksort-based sorting scheme and enumeration sorting scheme can be developed for sorting large distributed files on the hypercube and de Bruijn networks. Both of our sorting algorithms outperform the existing distributed sorting schemes in terms of both message complexity and communication delay.

Improving the Performance of All-optical WDM Networks based on Light-path Reservation

In this paper, three methods are proposed to improve the performance of all-optical WDM networks based on the light-path reservation scheme. These are wavelength conversion, multiple fibers and two-path routing. We begin by developing analytical models for static-routing networks based on the nonblocking centralized switch, bi-directional Manhattan Street network and de Bruijn network topologies. Analytical results show that in most cases, the multiple fibers and wavelength conversion schemes give the best performance, in terms of lowest blocking probability, for the nonblocking centralized network at light and heavy loads respectively. The reverse is true for the bi-directional Manhattan Street and de Bruijn networks. The choice depends on the values of the parameters such as network load and reservation level. The two-path routing method offers moderate improvement in performance for the de Bruijn network topology. In addition, there exist optimum reservation levels for attaining minimum blocking probabilities. The advantage of the three schemes is moderate in the centralized switch, and slightly less in the de Bruijn network. However, these schemes offer significant performance improvement for the bidirectional Manhattan Street network.

Comparative Study of Product Networks

The Cartesian product of interconnection networks has been investigated recently as a method for combining desirable properties of component networks. This paper presents a unified framework for obtaining and comparing properties of a virtually unlimited number of product networks. This work complements results appeared in the literature for product networks and conducts a comparative study between several networks including hypercubes, meshes, star graphs, deBruijn networks, product-shuffle networks, hyper-Petersen networks, mesh-connected-trees, hyper-deBruijn networks, dBCubes, star–cube networks, and hyperstar networks. The comparison is based on network scalability, broadcasting cost, embedding of other topologies, VLSI layout, cost/performance ratio, and other static parameters such as degree, diameter, and number of links.

A NEW FAMILY OF EXTREMAL INTERCONNECTION NETWORKS

We extensively discuss a new interconnection network topology, denoted by ϒ(n,r). Firstly, the ϒ(n,2) network is shown to provide average cost 3 log 2 n while providing superior fault tolerance characteristics. It is defined over any natural number of nodes n using 2n-3 edges for an average degree of 4 and has diameter no greater than k=⌈ log 2n⌉ with average diameter as small as [Formula: see text]. The network is planar and has cyclomatic number n-2. For n=2t the unbounded maximum degree is 2 log 2 n-1 believed indicative of generally a maximum unbounded degree O( log 2n). The bisection width ranges from 3 when n=2t to t+1 when n=2t+1. Secondly, we provide the ϒ*(n,r) network of bounded degree 2r. For n=rt the ϒ*(n,r) network has asymptotically better average cost than the general deBruijn(r,t) network while also maintaining planarity and cyclomatic property of ϒ(n,2). The ϒ family exhibits unique extremal properties of both theoretical interest and practical importance.

A new architecture and a new metric for lightwave networks

The notion of a logically routed network was developed to overcome the bottlenecks encountered during the design of a large purely optical network. In the last few years, researchers have proposed the use of torus. Perfect shuffle, hypercube, de Bruijn graph, Kautz graph, and Cayley graph as an overlay structure on top of a purely optical network. All these networks have regular structures. Although regular structures have many virtues, it is often difficult in a realistic setting to meet these stringent structural requirements. In this paper, we propose generalized multimesh (GM), a semiregular structure, as an alternate to the proposed architectures. In terms of simplicity of interconnection and routing, this architecture is comparable to the torus network. However, the new architecture exhibits significantly superior topological properties to the torus. For example, whereas a two-dimensional (2-D) torus with N nodes has a diameter of /spl Theta/(N/sup 0.5/), a generalized multimesh network with the same number of nodes and links has a diameter of /spl Theta/(N/sup 0.25/). In this paper, we also introduce a new metric, flow number, that can be used to evaluate topologies for optical networks. For optical networks, a topology with a smaller flow number is preferable, as it is an indicator of the number of wavelengths necessary for full connectivity. We show that the flow numbers of a 2-D torus, a multimesh, and a de Bruijn network, are /spl Theta/(N/sup 1.5/), /spl Theta/(N/sup 1.25/), and /spl Theta/(N log N), respectively, where N is the number of nodes in the network. The advantage of the generalized multimesh over the de Bruijn network lies in the bet that, unlike the de Bruijn network, this network can be constructed for any number of nodes and is incrementally expandable.

On new architectures for lightwave networks

In this paper, we propose two different architectures, the multi-mesh (MM) and the incomplete multi-mesh (IMM), for use in wavelength division multiplexed optical networks. These architectures can be deployed as a physical topology for single hop or a logical topology for multihop networks. In terms of simplicity of interconnection and routing, these architectures are comparable to the regular mesh and the torus networks. However, the new architectures exhibit significantly superior topological properties than the mesh and the torus. For example, whereas a two-dimensional torus with N nodes has a diameter of Θ( N 0.5), an MM network with the same number of nodes and links has a diameter of Θ( N 0.25). The IMM can be constructed for any number of nodes and is incrementally expandable. We provide results of our simulation studies for the call blocking probabilities for the MM network. The advantage of the IMM over the de Bruijn network lies in the fact that unlike the de Bruijn network, this network can be constructed for any number of nodes and is incrementally expandable.

Shortest path routing and fault-tolerant routing on de Bruijn networks

In this paper, we study the routing problem for the undirected binary de Bruijn interconnection network. Researchers have never proposed a shortest path routing algorithm on the undirected binary de Bruijn network. We first propose a shortest path routing algorithm, whose time complexity in the binary de Bruijn network of 2m nodes is O(m2). Then, based on our shortest path routing algorithm, we propose two fault-tolerant routing schemes. It is assumed that at most one node fails in the network. In our schemes, two node-disjoint paths are found. Our first fault-tolerant routing algorithm guarantees that one of the two paths is the shortest path, and the other is of length at most m + log2 m + 4. Our second algorithm can find two node-disjoint paths with lengths at most m and m + 4, respectively, if the shortest path is not required in the fault-tolerant routing. © 2000 John Wiley & Sons, Inc.

Hierarchical Networks for Optical Communications

ShuffleNet and de Bruijn networks have been proposed as multihop lightwave networks based on wavelength division multiplexing (WDM). With multihop lightwave networks, few fixed wavelength transmitters/receivers are assigned to each user, eliminating the need for wavelength agility and pretransmission coordination. These networks have been shown to be very effective for uniform traffic. For communications with high locality, we propose two-level hierarchical networks. At the first level, each cluster of users can be connected either via a ShuffleNet (SH) or a de Bruijn network (dB). At the second level, all the clusters in the system can be connected by two rings in opposite directions (SH/Ring and dB/Ring), a de Bruijn network (dB/dB), or a ShuffleNet (SH/SH). The performance of ShuffleNet, de Bruijn networks, and the hierarchical networks SH/Ring, dB/Ring, dB/dB, and SH/SH is analyzed. For communications with a high locality, the hierarchical networks are shown to be very effective.