Arbitrary Size Benes Networks

The Benes network is a rearrangeable nonblocking network which can realize any arbitrary permutation. Overlall, the r-dimensional Benes network connects 2r inputs to 2r outputs through 2r - 1 levels of 2 × 2 switches. Each level of switches consists of 2r - 1 switches, and hence the size of the network has to be a power of two. In this paper, we extend Benes networks to arbitrary sizes. We also show that the looping routing algorithm used in Benes networks can be slightly modified and applied to arbitrary size Benes networks.

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Design and Implementation of Rearrangable Non-Blocking Switching Network in VLSI

International Journal of Recent Technology and Engineering - 2 ◽

10.35940/ijrte.b1356.0982s1119 ◽

2019 ◽

Vol 8 (2S11) ◽

pp. 2858-2863

Keyword(s):

Interconnection Network ◽

The Other ◽

Switching Network ◽

Low Latency ◽

Multistage Interconnection Network ◽

Design And Implementation ◽

Benes Network ◽

Benes Networks

The main goal of this article is to implement an effective Non-Blocking Benes switching Network. Benes Switching Network is designed with the uncomplicated switch modules & it’s have so many advantages, small latency, less traffic and it’s required number of switch modules. Clos and Benes networks are play a key role in the class of multistage interconnection network because of their extensibility and mortality. Benes network provides a low latency when compare with the other networks. 8x8 Benes non blocking switching network is designed and synthesized with the using of Xilinx tool 12.1.

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Introduction and Analysis of Optimal Routing Algorithm in Benes Networks

Procedia Computer Science ◽

10.1016/j.procs.2014.11.068 ◽

2014 ◽

Vol 42 ◽

pp. 313-319 ◽

Cited By ~ 3

Author(s):

Abbas Karimi ◽

Kiarash Aghakhani ◽

Seyed Ehsan Manavi ◽

Faraneh Zarafshan ◽

S.A.R. Al-Haddad

Keyword(s):

Routing Algorithm ◽

Optimal Routing ◽

Benes Networks

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A partially adaptive routing algorithm for Benes network on chip

2009 2nd IEEE International Conference on Computer Science and Information Technology ◽

10.1109/iccsit.2009.5234772 ◽

2009 ◽

Cited By ~ 3

Author(s):

Jing Zhang ◽

Huaxi Gu

Keyword(s):

Routing Algorithm ◽

Adaptive Routing ◽

Network On Chip ◽

Benes Network ◽

On Chip

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ON ARBITRARY SIZE WAKSMAN NETWORKS AND THEIR VULNERABILITY

Parallel Processing Letters ◽

10.1142/s0129626402000999 ◽

2002 ◽

Vol 12 (03n04) ◽

pp. 287-296 ◽

Cited By ~ 12

Author(s):

B. BEAUQUIER ◽

E. DARROT

Keyword(s):

Fault Tolerance ◽

Arbitrary Size ◽

Benes Network ◽

One To One ◽

Permutation Networks

Motivated by problems in telecommunication satellites, we investigate rearrangeable permutation networks made of binary switches. A simple counting argument shows that the number of switches necessary to build a n × n rearrangeable networks (i.e. capable of realizing all one-to-one mappings of its n inputs to its n outputs) is at least ⌈ log 2 (n!) ⌉ = n log 2 n - n log 2 e + o(n) as n → ∞. For n = 2r, the r-dimensional Beneš network gives a solution using [Formula: see text] switches. Waksman, and independently Goldstein and Leibholz, improved these networks using n log 2 n - n + 1 switches. We provide an extension of this result to arbitrary values of n, using [Formula: see text] switches. Finally the fault-tolerance issue of these networks is discussed.

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Improved Arbitrary size Benes Network

International Journal of Computer Applications ◽

10.5120/7482-0566 ◽

2012 ◽

Vol 48 (21) ◽

pp. 30-34

Author(s):

Gaurav Kumar ◽

Sandeep Sharma

Keyword(s):

Arbitrary Size ◽

Benes Network

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Least Common Ancestor Networks

VLSI Design ◽

10.1155/1995/53054 ◽

1995 ◽

Vol 2 (4) ◽

pp. 353-364 ◽

Cited By ~ 6

Author(s):

Isaac D. Scherson ◽

Chi-Kai Chien

Keyword(s):

Common Ancestor ◽

Routing Algorithm ◽

Routing Algorithms ◽

Routing Strategy ◽

Iterative Analysis ◽

Simulation Results ◽

Randomized Routing ◽

Permutation Routing ◽

Benes Networks

Least Common Ancestor Networks (LCANs) are introduced and shown to be a class of networks that include fattrees, baseline networks, SW-banyans and the router networks of the TRAC 1.1 and 2.0 and the CM-5. Some LCAN properties are stated and the circuit-switched permutation routing capabilities of an important subclass are analyzed. Simulation results for three permutation classes verify the accuracy of an iterative analysis for a randomized routing strategy. These results indicate that the routing strategy provides highly predictable router performance for all permutations. An off-line routing algorithm is also given, and it is shown how to realize certain classes of permutations by adapting Nassimi and Sahni's, and Raghavendra and Boppana's self-routing algorithms for Benes networks.

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Adaptive Routing Strategy for Large Scale Rearrangeable Symmetric Networks

Evolving Developments in Grid and Cloud Computing ◽

10.4018/978-1-4666-0056-0.ch015 ◽

2012 ◽

pp. 212-222

Author(s):

Amitabha Chakrabarty ◽

Martin Collier ◽

Sourav Mukhopadhyay

Keyword(s):

Large Scale ◽

Blocking Probability ◽

Routing Algorithm ◽

Adaptive Routing ◽

Low Complexity ◽

Deterministic Algorithms ◽

The Status ◽

Extensive Computation ◽

Benes Networks ◽

Symmetric Networks

This paper proposes an adaptive unicast routing algorithm for large scale symmetric networks comprising 2 × 2 switch elements such as Beneš networks. This algorithm trades off the probability of blocking against algorithm execution time. Deterministic algorithms exploit the rearrangeability property of Beneš networks to ensure a zero blocking probability for unicast connections, at the expense of extensive computation. The authors’ algorithm makes its routing decisions depending on the status of each switching element at every stage of the network, hence the name adaptive routing. This method provides a low complexity solution, but with much better blocking performance than random routing algorithms. This paper presents simulation results for various input loads, demonstrating the tradeoffs involved.

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On Topological Indices for New Classes of Benes Network

Journal of Mathematics ◽

10.1155/2021/6690053 ◽

2021 ◽

Vol 2021 ◽

pp. 1-7

Author(s):

Aftab Hussain ◽

Muhammad Numan ◽

Nafisa Naz ◽

Saad Ihsan Butt ◽

Adnan Aslam ◽

...

Keyword(s):

Molecular Graph ◽

Quantitative Structure Activity Relationship ◽

Topological Indices ◽

Structure Property ◽

Structure Activity ◽

Randić Connectivity Index ◽

Structure Property Relationship ◽

Benes Network ◽

Benes Networks ◽

Atom Bond

Topological indices (TIs) transform a molecular graph into a number. The TIs are a vital tool for quantitative structure activity relationship (QSAR) and quantity structure property relationship (QSPR). In this paper, we constructed two classes of Benes network: horizontal cylindrical Benes network HCB r and vertical cylindrical Benes network obtained by identification of vertices of first rows with last row and first column with last column of Benes network, respectively. We derive analytical close formulas for general Randić connectivity index, general Zagreb, first and the second Zagreb (and multiplicative Zagreb), general sum connectivity, atom-bond connectivity ( VCB r ), and geometric arithmetic ABC index of the two classes of Benes networks. Also, the fourth version of GA and the fifth version of ABC indices are computed for these classes of networks.

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