M. Samatham and D. Pradhan. The de bruijn multiprocessor network: a versatile parallel processing and sorting network for VLSI. EEE Trans. on Computers, 38(4), 1989.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....attention; see, e.g. the survey article of Monien and Sudborough [10] and the literature mentioned there. De Bruijn graphs are popular communication networks for parallel computers because they feature several nice properties such as fixed node degree and small diameter (for more details cf. [4, 15, 16]) The problem of studying embeddings of hypercubes, grids and tori into de Bruijn graphs was initiated by Heydemann, Opatrny, and Sotteau [7, 8] who obtained a variety of results on embedding hypercubes and 2 dimensional grids into de Bruijn graphs, while grids of higher dimension and tori were ....

M.R. Samatham and D.K. Pradhan. The de Bruijn Multiprocessor Network: A Versatile Parallel Processing and Sorting Network for VLSI. IEEE Trans. on Computers, Vol. 38, pages 567--581, April 1989.

....instead of working with a base 2 de Bruijn graph, Koorde can work with a base O(log n) de Bruijn graph. With such a graph, Koorde has fault tolerance and the number of routing hops is O( log n) log log n) which is optimal. 5 Related work We are not the first to use de Bruijn graphs in routing [1, 3, 13, 14], and concurrent with our work others have noted their application to DHTs [4] Compared to the related work, our primary contribution is how to simulate a lookup using a de Bruijn graph in a sparsely populated identifier space. Koorde s approach of using de Bruijn graphs is different than D2B s ....

SAMATHAM, M., AND PRADHAM, D. The de bruijn multiprocessor network: a versatile parallel processing and sorting network for VLSI. IEEE Trans. on Computers 38, 4 (1989), 567--581.

.... Opatrny, Sotteau [6, 7] For general information on interconnection networks and, in particular, on containment and embedding results, we refer to [2, 3, 9, 10] and the literature mentioned there; for applications, e.g. in the field of parallel image processing and pattern recognition, see [5, 11, 12, 13]. All graphs considered in this paper are simple, i.e. have no loops or multiple edges. If G is a graph, then V (G) and E(G) denote the set of vertices and the set of edges of G, respectively. Our terminology is standard; for graph theoretic terminology not explained here, we refer to [4] For ....

M.R. Samatham and D.K. Pradhan, "The de Bruijn multiprocessor network: a versatile parallel processing and sorting network for VLSI", IEEE Transactions on Computers, vol. 38, no. 4, pp. 567--581, 1989.

....attention; see, e.g. the survey article of Monien and Sudborough [7] and the literature mentioned there. De Bruijn graphs are popular communication networks for parallel computers because they feature several nice properties such as fixed node degree and small diameter (for more details cf. [3, 11, 12]) The problem of studying embeddings of hypercubes, grids and tori into de Bruijn graphs was initiated by Heydemann, Opatrny, and Sotteau [5, 6] who obtained a variety of results on embedding hypercubes and 2 dimensional grids into de Bruijn graphs, while grids of higher dimension and tori were ....

M.R. Samatham and D.K. Pradhan. The de Bruijn Multiprocessor Network: A Versatile Parallel Processing and Sorting Network for VLSI. IEEE Trans. on Computers, Vol. 38, pages 567--581, April 1989.

....and tori are considered only briefly. In contrast, in the paper [4] the emphasis is on tori. For definitions, see below. De Bruijn graphs are popular communication networks for parallel computers because they feature several nice properties such as fixed node degree and small diameter ( 5] [6], 7] For information on the role of de Bruijn networks in parallel image processing and pattern recognition, see e.g. 8] In the present paper, for Cartesian products G = G 1 Theta : Theta Gm (m 2) of non trivial connected graphs G i and the n dimensional base B de Bruijn graph D = DB ....

M.R. Samatham and D.K. Pradhan, "The de Bruijn multiprocessor network: a versatile parallel processing and sorting network for VLSI", IEEE Transactions on Computers, vol. 38, no. 4, pp. 567--581, 1989.

.... x 1 Delta Delta Delta xD x 2 Delta Delta Delta xD y 1 x 3 Delta Delta Delta xD y 1 y 2 Delta Delta Delta y 1 Delta Delta Delta y D : We refer the reader to one of the two recent surveys concerning de Bruijn networks written by Bermond and Peyrat [4] and Samatham and Pradhan [13] or to the recent book of Leighton [10] In this paper, we analyze the mean eccentricity of these graphs. The eccentricity of a vertex X is defined [6] as the distance to the farthest node from this vertex: e(X) maxfd(X; Y ) Y 2 V g. We define the mean eccentricity of a vertex X , denoted ....

M.R. Samatham and D.K. Pradhan, "The de Bruijn multiprocessor network: a versatile parallel processing and sorting network for VLSI", IEEE Trans. on Comp., 38, No. 4, pp. 567--581, 1989. 32

....1) is Hamiltonian cycle of K(d; D) and the same holds for B(d; D) De Bruijn (di)graphs, and the binary ones in particular, received more attention from the researchers than Kautz digraphs. Various results on nontrivial embeddings and emulations have been published in last few years (see, e.g. [1, 8, 13, 14]) Neither alphabet nor line digraph definitions allow incrementally expandable digraphs. Congruent arithmetics enables to define generalized K B digraphs for any number of vertices. 2.4 Generalized K B digraphs Let GK(d; n) and GB(d; n) denote the generalized Kautz and de Bruijn digraph, ....

M. R. Samathan and D. K. Pradhan. The de Bruijn multiprocessor network: A versatile parallel processing and sorting network for VLSI. IEEE Transactions on Computers, C38 (4):567--581, Apr. 1989.

....graphs. These graphs are known to be able to emulate the much larger butterfly graph and its butterflyoriented relatives efficiently on a large class of computations [2] 39] hence, these graphs have been widely proposed as interconnection networks for parallel architectures [6] [31], 33] 36] The order n de Bruijn graph D n is usually presented as a directed graph. The digraph D n has node set Nodes(D n ) Z n 2 ; its arcs lead every node fix, where x 2 Z n Gamma1 2 and fi 2 Z 2 to nodes xfi and x fi. Because D n has 2 n nodes, each of indegree and outdegree 2, ....

M.R. Samatham and D.K. Pradhan (1989): The de Bruijn multiprocessor network: a versatile parallel processing and sorting network for VLSI. IEEE Trans. Comp. 38, 567-581.

....path. 952 1. Introduction The generalized de Bruijn network is based on the de Bruijn digraph [8] 3] This network received much attention from researchers because it possesses several interesting properties which makes it suitable for many parallel processing applications [3] 6] 8] [9]. For instance, Samathan and Pradhan [9] have shown that the de Bruijn network can efficiently embed several other important architectures such as the linear array, ring, 2 D mesh, cube connected cycles, complete binary tree, and tree machine. Thus, the network can efficiently run the important ....

.... generalized de Bruijn network is based on the de Bruijn digraph [8] 3] This network received much attention from researchers because it possesses several interesting properties which makes it suitable for many parallel processing applications [3] 6] 8] 9] For instance, Samathan and Pradhan [9], have shown that the de Bruijn network can efficiently embed several other important architectures such as the linear array, ring, 2 D mesh, cube connected cycles, complete binary tree, and tree machine. Thus, the network can efficiently run the important algorithm classes best suited for these ....

[Article contains additional citation context not shown here]

M. R. Samathan and D. K. Pradhan, "The de Bruijn Multiprocessor Network: A Versatile Parallel Processing and Sorting Network for VLSI," IEEE Trans. on Computers, pp. 567-581. vol. 38, No. 4, April, 1989.

....of our study. Section 3 presents our emulation strategy in a topology independent fashion. Section 4 describes and analyzes our emulations on three substantively different array topologies that have been used in computer architectures: the hypercube [27] Section 4. 1) the de Bruijn network [22] (Section 4.2) and the extended coterie network, a mesh with a reconfigurable bus which abstracts the UMass CAAPP architecture [30] Section 4.3. In Section 5, we show that the operational performance of our emulation based multigauging is superior to having the host A perform k bit operations ....

M.R. Samatham and D.K. Pradhan, The de Bruijn Multiprocessor Network: A Versatile Parallel Processing and Sorting Network for VLSI, IEEE Trans. Computers, vol. 38, pp. 567581, 1989.

....has as its vertices all those strings of length D over the alphabet f0; 1; dg in which consecutive characters are distinct; 11 there is an arc from a vertex a 1 a 2 a 3 : a D to all vertices a 2 a 3 : a D a with a from f0; 1; dg and distinct from aD . It is easy to see (cf. 5] 16] [24]) that both B(d; D) and K(d; D) are (d; D) digraphs. Moreover, the digraph B(d; D) has d D vertices and the digraph K(d; D) has d D d D Gamma1 vertices. We immediately obtain, via the proof of Proposition 3, large (balanced) 2d 2; D)C digraphs. However, we were able to prove (see [6] ....

M.R. Samatham and D.K. Pradhan, The de Bruijn multiprocessor network: A versatile parallel processing and sorting network for VLSI, IEEE Trans. Comput., vol. C--38, 4, pp. 567--581, 1989.

....constructed as follows [21] For every vertex v 2 V(G) there are two vertices v and v Gamma 2 V( G) The vertices v i and v Gamma j are adjacent in G, if and only if the vertices v i and v j are adjacent in G. Let G be the bipartite double of the de Bruijn graph (see [15] or [53]) of maximum degree r (r is even) and diameter D Gamma 1. Then G is regular of degree r, has 2(r=2) D Gamma1 vertices and diameter D. The dual hypergraph of G is a (2; D; r) hypergraph with 2(r=2) D vertices. An extension of the bipartite double of de Bruijn graphs, is the C s graphs ....

M.R. Samatham and D.K. Pradhan. The de Bruijn multiprocessor network: a versatile parallel processing and sorting network for VLSI. IEEE Trans. on Computers, 38:567--581, 1989. (corrections in IEEE Trans. on Computers, vol. 40, pp. 122-123).

.... x 1 Delta Delta Delta xD x 2 Delta Delta Delta xD y 1 x 3 Delta Delta Delta xD y 1 y 2 Delta Delta Delta y 1 Delta Delta Delta y D : We refer the reader to one of the two recent surveys concerning de Bruijn networks written by Bermond and Peyrat [4] and Samatham and Pradhan [13] or to the recent book of Leighton [10] 2 In this paper, we analyze the mean eccentricity of these graphs. The eccentricity of a vertex X is defined [6] as the distance to the farthest node from this vertex: e(X) maxfd(X; Y ) Y 2 V g. We define the mean eccentricity of a vertex X , ....

M.R. Samatham and D.K. Pradhan, "The de Bruijn multiprocessor network: a versatile parallel processing and sorting network for VLSI", IEEE Trans. on Comp., 38, No. 4, pp. 567--581, 1989. 34

....As a result, several families of networks with large number of processors for given degree and diameter have been proposed. Surveys on this topic can be found in [1] 2] 6] and [8] Among them, de Bruijn and Kautz networks appear to have many other desirable properties (for details see [7] [17]) Classical definition of the de Bruijn networks is based on alphabets. These networks can be generalized for any number of processors by using arithmetic congruences (see [13] 16] When the bus size is taken into account as an extra parameter, the problem becomes more complicated. There are ....

M.R. Samatham and D.K. Pradhan. The de Bruijn multiprocessor network: a versatile parallel processing and sorting network for VLSI. IEEE Trans. on Computers, 38:567--581, 1989. (corrections in IEEE Trans. on Computers, vol. 40, pp. 122-123). 20

.... x 1 Delta Delta Delta xD x 2 Delta Delta Delta xD y 1 x 3 Delta Delta Delta xD y 1 y 2 Delta Delta Delta y 1 Delta Delta Delta y D : We refer the reader to one of the two recent surveys concerning de Bruijn networks written by Bermond and Peyrat [5] and Samatham and Pradhan [14] or to the recent book of Leighton [11] In this paper, we analyze the mean eccentricity of these graphs. The eccentricity of a vertex X is defined [7] as the distance to the farthest node from this vertex: e(X) maxfd(X; Y ) Y 2 V g. We define the mean eccentricity of a vertex X, denoted ....

M.R. Samatham and D.K. Pradhan, "The de Bruijn multiprocessor network: a versatile parallel processing and sorting network for VLSI", IEEE Trans. on Comp., 38, No. 4, pp. 567--581, 1989.

.... to dynamic routing on the d way shuffle [9] On the n way shuffle (d = n) deterministic sorting, by embedding Batcher s sorting network, achieves O(n 2 ) delay [229] probabilistic two phase routing is asymptotically optimal [236] and off line BPC, Omega, and Inverse Omega routing is optimal [275]. Wei and Hsu have provided upper and lower bounds for deterministic oblivious permutation routing and sorting on the directed version of the de Bruijn network [112] The undirected n dimensional shuffle exchange has N = 2 n nodes, diameter 2n Gamma 1, and degree 3. A node represented by a ....

Samatham, M. R., and Pradhan, D. K. The de Bruijn multiprocessor network: A versatile parallel processing and sorting network for VLSI. IEEE Trans. Comput. C-38 (4), 1989, pp. 567--581.

....also have more paths between pairs of nodes, which permits more adaptivity and fault tolerance. A class of shuffle networks known as de Bruijn (dB) graphs have become popular recently. They are suitable for large network and can be defined for any number of nodes, including prime numbers [61]. For a specific node degree, dB networks, in most cases, have the smallest diameter compared to the contemporary network topologies. Formally, a unidirectional dB network can be defined as follows [61] Definition 3: An r radix unidirectional de Bruijn digraph dBD(r; r m ) has the total number ....

....suitable for large network and can be defined for any number of nodes, including prime numbers [61] For a specific node degree, dB networks, in most cases, have the smallest diameter compared to the contemporary network topologies. Formally, a unidirectional dB network can be defined as follows [61]. Definition 3: An r radix unidirectional de Bruijn digraph dBD(r; r m ) has the total number of nodes N = r m and the address of a node X is represented as (x m Gamma1 ; xm Gamma2 ; x 0 ) where x i 2 f0; 1; r Gamma 1)g for 0 i m Gamma 1. Its neighboring nodes are (x m Gamma2 ; ....

M. R. Samatham and D. K. Pradhan, "The de Bruijn Multiprocessor Network: A versatile parallel processing and sorting network for VLSI," IEEE Trans. on Computers, C-38, pp. 567-581, Apr. 1989.

....networks with many narrow channels. 1.2 Network Topologies Three topologies are commonly used in current multiprocessors: mesh, torus, and hypercube. As discussed later, such topologies are often referred to as k ary n cubes. 8 Other topologies have been proposed, such as de Bruijn networks [84] and cubeconnected cycles [83] As far as we know, no commercial multiprocessors use these topologies. 1.2.1 Hypercube A hypercube has two processing nodes in each dimension, so a hypercube can be characterized as a 2 ary n cube, where n is the dimension. For example, a 2 ary 8 cube is an 8D ....

M. R. Samatham and D. K. Pradhan. The De Bruijn Multiprocessor Network: A Versatile Parallel Processing and Sorting Network for VLSI. IEEE Transactions on Computers, 38(4):567--581, April 1989.

.... There are a number of applications where we need such constant degree networks; in VLSI design we need To appear in Journal of Circuits, Systems and Computers them for area efficient layout [CAB93] there are applications where the computing nodes can have only a fixed number of I O ports[SP89]. Constant degree network graphs are of considerable practical importance since De Bruijn graphs are being used for designing a 8096 node multiprocessor at JPL for the Galileo project [Pra91] There exist graphs in the literature with bounded node degree; most popular among them are De Bruijn ....

M. R. Samatham and D. K. Pradhan. The De Bruijn multiprocessor network: a versatile parallel processing and sorting network for VLSI. IEEE Transactions on Computers, 38(4):567-- 581, April 1989.

....of edges per node, a low diameter, a fast shortest path routing and defines a natural connection structure for FFT applications. Especially this last property makes it a good candidate for the interconnection network of parallel computers. Many results concerning the de Bruijn network are given in [Lei92,SP89,BP89]. Nevertheless for the bisection width of the de Bruijn there is still a huge gap between known upper and lower bounds. If we define dB(n) to be the de Bruijn network of dimension n (with 2 n nodes) we already know that 2 n n fi(dB(n) 4 Delta 2 n n : The upper bound is derived by ....

M.R. Samatham and D.K. Pradhan. The de bruijn multiprocessor network: A versatile parallel processing and sorting network for vlsi. IEEE Transactions on Computers, 38(4):567--581, 1989.

....with the size of the graph (the number of vertices) either logarithmically or sub logarithmically. This property can make the use of these graphs prohibitive for networks with large number of vertices [6] Fixed vertex degree networks are also very important from VLSI implementation point of view [7]; there are applications where the computing vertices in the interconnection network can have only a fixed number of I O ports [6] As a matter of fact a large multiprocessor (with 8096 vertices) is being built by JPL around the binary De Bruijn graphs [8] which are almost regular network graphs ....

M. R. Samatham and D. K. Pradhan. The De Bruijn multiprocessor network: a versatile parallel processing and sorting network for VLSI. IEEE Transactions on Computers, 38(4):567--581, April 1989.

....and essential component in designing any distributed system. Networks, in which degree of the nodes increases with the size of the network, are not suitable for applications involving large number of nodes [CAB93] Fixed node degree networks are also needed from VLSI implementation point of view [SP89]; there are applications where the computing nodes in the interconnection network can have only a fixed number of I O ports [CAB93] There are a few network graphs in the literature [PR82, LS82, PN93] where the node degree does not increase with network size; most popular among them are the De ....

M. R. Samatham and D. K. Pradhan. The De Bruijn multiprocessor network: a versatile parallel processing and sorting network for VLSI. IEEE Transactions on Computers, 38(4):567--581, April 1989.

....It points out the fact that the two bounds are not very far apart for small dimensions m. Actually, for m 4, i.e. up to 64 nodes, our broadcasting algorithm turns out to be optimal. DeBruijn networks have been proposed as a possible alternative for designing large interconnection networks [BP89] [SP89]. Broadcasting in these graphs was considered in [BP88] and [HOS91] In [BP88] an upper bound of 1:5m 1:5 for the (binary) deBruijn graph of dimension m, DB(m) was stated. A lower bounds of b(DB(m) 1:1374m can be derived from [LP88] Applying the same techniques as for the butterfly ....

M.R. Samatham, D.K. Pradhan, "The de Bruijn multiprocessor network: a versatile parallel procesing and sorting network for VLSI", IEEE Transactions on Computers, vol. 38, no. 4, pp. 567-581, 1989.

....This is due to the existence of self loops 23 which carry no traffic. The maximum deflection penalty in a de Bruijn network is log p N 1 since a packet can travel back to the point where it was deflected in at most log p N steps. Communication networks based on de Bruijn graphs are discussed in [SaP89, EsH85, SiR91]. 0 1 2 3 4 5 6 7 0 1 2 3 4 5 6 7 From To 1 2 0 1 2 3 4 5 6 7 0 1 2 3 4 5 6 7 2 3 3 3 1 1 2 2 2 2 2 2 2 1 1 3 3 3 3 2 2 1 1 1 1 2 2 3 3 3 1 1 2 2 2 2 2 2 2 1 1 3 3 3 2 2 1 13 7 = 1.86 14 7 = 2.00 13 7 = 1.86 14 7 = 2.00 2 1 14 7 = 2.00 2 14 7 = 2.00 14 7 = 2.00 14 7 = 2.00 Avg = 1.96 2 1 2 3 ....

M.R. Samatham, D.J. Pradhan, "The De Bruijn Multiprocessor Network: A Versatile Parallel Processing and Sorting Network for VLSI", IEEE Trans. on Computers, 38, 4 (April 1989), 567--581.

....y 2 : y k provided that x 2 x 3 : x k = y 1 y 2 : y k Gamma1 . This graph, known as a (directed) binary de Bruijn graph or shift register graph, is illustrated in Figure 3 for k = 3. Parallel computers based on de Bruijn graphs have recently been suggested as alternatives to hypercubes [19]. When it is notationally convenient, we will denote the vertices of B k as 0; 1; 2 k Gamma 1, using the decimal equivalent of their binary k tuple. With this notation, vertex j has an edge directed from it to vertex 2j and to vertex 2j 1, where these numbers are taken modulo 2 k . ....

D.K. Pradhan and M.R. Samatham, "The de Bruijn multiprocessor network: a versatile parallel processing and sorting network for VLSI", IEEE Trans. Computers 38 (1989) pp. 567-581.

....edges per node, a low diameter, a fast shortest path routing and defines a natural connection structure for FFT applications. Especially this last property makes it a good candidate for the interconnection network of parallel computers. Many results concerning the de Bruijn network are given in [Lei92, SP89, BP89]. Nevertheless for the bisection width of the de Bruijn there is still a huge gap between known upper and lower bounds. If we define dB(n) to be the de Bruijn network of dimension n (with 2 n nodes) we know ( Lei92] that 2 n =n fi(dB(n) 4 Delta 2 n =n: The upper bound is derived by ....

M.R. Samatham and D.K. Pradhan. The de Bruijn Multiprocessor Network: A Versatile Parallel Processing and Sorting Network for VLSI. IEEE Transactions on Computers, 38(4):567--581, 1989.

....the first symbol s[1] of the string s, removes this symbol from the header, and routes in the direction obtained by some simple local computation based on s[1] When the string is empty, the message must be locally consumed. This definition is typically used to route on de Bruijn networks B(d; D) [9, 67]. In this case, the string is a word of length D on an alphabet of d letters: on node x, R(x; s) s[1] assuming that the d output ports of each node are labeled by the d letters of the alphabet. Multi dependent. A multi dependent routing function on a digraph G is a function R : V Theta V ....

M. Samatham and D. Pradhan, The de Bruijn multiprocessor network: a versatile parallel processing and sorting network for VLSI, IEEE Transactions on Computers, 38 (1989), pp. 567-- 581.

....studied in [1] A number of optimal routing algorithms have been proposed for the de Bruijn network, the CCC, and the butterfly network, but none seems to be easily adaptable to work for the shuffle exchange network. Guha and Sen [4] gave an optimal algorithm for the undirected de Bruijn graph [10, 11]. Liu and Lee [7] gave an optimal routing algorithm for the generalized de Bruijn digraph [3] Meliksetian and Chen [9] gave an optimal routing algorithm for the CCC. Vadapalli and Srimani [13] gave an optimal routing algorithm for the butterfly network (although they did not realize that their ....

M.R. Samatham and D.K. Pradhan, "The de Bruijn multiprocessor network: A versatile parallel processing and sorting network for VLSI," IEEE Transactions on Computers, 38(4):567--581, April 1989.

.... are not so suitable for area efficient layout; we need constant degree networks (where the degree of a node does not change with the size of the network) There are also important applications for which the computing nodes in the interconnection network can have only a fixed number of I O ports [SP89, CAB93]. There are graphs in the literature that have constant node degrees, like the Cube Connected Cycles [PV81] where the degree of any node is 3 irrespective of the size of the graph. These cube connected cycle graphs can be viewed as Cayley graphs [CCSW85] There also exist graph topologies in the ....

M. R. Samatham and D. K. Pradhan. The De Bruijn multiprocessor network: a versatile parallel processing and sorting network for VLSI. IEEE Transactions on Computers, 38(4):567--581, April 1989.

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M. Samatham and D. Pradhan. The de bruijn multiprocessor network: a versatile parallel processing and sorting network for VLSI. EEE Trans. on Computers, 38(4), 1989.

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D.K. Pradhan and M.R. Samatham, "The de Bruijn multiprocessor network: a versatile parallel processing and sorting network for VLSI", IEEE Trans. Computers 38 (1989) pp. 567-581.

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M.R. Samatham and D.K. Pradhan, "The de Bruijn multiprocessor network: A versatile parallel processing and sorting network for VLSI," IEEE Transactions on Computers, 38(4)8 April 1989.

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M.R. Samatham and D.K. Pradhan, The de Bruijn multiprocessor network: A versatile parallel processing and sorting network for VLSI, IEEE Trans. Comput., vol. C--38, 4, pp. 567--581, 1989.

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M.R. Samatham and D.K. Pradhan, "The de Bruijn multiprocessor network: a versatile parallel processing and sorting network for VLSI", IEEE Trans. on Comp., 38, No. 4, pp. 567--581, 1989. 34

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M. Samatham and D. Pradhan. The de bruijn multiprocessor network: a versatile parallel processing and sorting network for VLSI. EEE Trans. on Computers, 38(4), 1989.

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M. Samatham and D. K. Pradhan, The De Bruijn multiprocessor networks: A versatile parallel processing and sorting network for VLSI, IEEE Trans. Computers, (1989), vol. 38, no. 4, pp. 567-581.

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M.R. Samatham and D.K. Pradhan, The de Bruijn multiprocessor network: A versatile parallel processing and sorting network for vlsi, IEEE Trans Comput 38 (1989), 567--581.

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M.R. Samatham, D.K. Pradhan, "The de Bruijn multiprocessor network: a versatile parallel processing and sorting network for VLSI", IEEE Transactions on Computers, Vol. 38, No. 4, pp. 567-581, 1989.

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