Reverse Banyan Network Research Articles

A new self-routing multicast network

In this paper, we propose a design for a new self-routing multicast network which can realize arbitrary multicast assignments between its inputs and outputs without any blocking. The network design uses a recursive decomposition approach and is based on the binary radix sorting concept. All functional components of the network are reverse banyan networks. Specifically, the new multicast network is recursively constructed by cascading a binary splitting network and two half-size multicast networks. The binary splitting network, in turn, consists of two recursively constructed reverse banyan networks. The first reverse banyan network serves as a scatter network and the second reverse banyan network serves as a quasisorting network. The advantage of this approach is to provide a way to self-route multicast assignments through the network and a possibility to reuse part of network to reduce the network cost. The new multicast network we design is compared favorably with the previously proposed multicast networks. It uses O(n log/sup 2/ n) logic gates, and has O(log/sup 2/ n) depth and O(log/sup 2/ n) routing time where the unit of time is a gate delay. By reusing part of the network, the feedback implementation of the network can further reduce the network cost to O(n log n).

ECI value generations in CSE-based distributors

In this letter we consider two efficient external control input (ECI) value generation methods for the controlled switching element (CSE)-based distributor, which is a new distributor structure that does not require the dummy address generation and extraction operations of the conventional distributors. The first method relies on the active packet counter and the ECI generator for ECI value generation, and the second method utilizes the intrinsic ECI generation property of the CSE-based reverse banyan network (RBN). The first method brings forth a flexible distributor structure, while the second method renders a very simple structure. In fact, the second method yields the so-called autonomous distributor, consisting only of a CSE-based RBN and a set of delays, which is perceived as the simplest among all available distributors. In addition, we introduce a modified version of the autonomous distributor which can speed up the connection-state setup process.

A new self-routing permutation network

In this paper, a self-routing permutation network based on a binary radix sorting network has been proposed. It has O(log/sup 2/ n) propagation delay and O(n log/sup 2/ n) hardware complexity with bit-parallel input. The hardware complexity can be reduced to O(n log n) with bit-serial input. The binary radix sorting network is recursively constructed by log n stages of bit sorting networks. The bit sorting network is then constructed by a proposed self-routing reverse banyan network. It has O(log n) propagation delay and O(n log n) hardware complexity. The proposed reverse banyan network has been fully verified by Verilog Hardware Description Language in logical level. The VLSI design of its switching elements is simple and regular.

Nonblocking properties of interconnection switching networks

Self-routing interconnection networks with their low processing-overhead delay and decentralized routing, are an attractive option for switching fabrics in high speed networks. These interconnection networks, however, realize only a subset of all possible input-output permutations in a non-blocking fashion. The non-blocking property of these networks is an extensively studied area in interconnection network theory field and efficient algorithms exist to check if any given permutation is passable by such networks without blocking. One of the most common interconnection network structures is the inverse omega network and is topologically equivalent to the reverse banyan network. The authors show how to check the passability by the inverse omega network of any given connection set and list some of the very general patterns passable by this network. They also show that the concentrate operation passable by the inverse omega network is just a special case of the more general alternate sequence operation that they show as being passable. These non-blocking properties will be useful for cell routing in switches built with blocking networks in parallel or in cascade. >

The composite banyan network

A new multipath multistage interconnection network called the composite banyan network is proposed. The network incorporates both the banyan and the reverse banyan networks and is constructed by superimposing the two. The basic building blocks in the composite banyan network are 3/spl times/3 switching elements with log/sub 2/N stages. A major advantage of the composite banyan network over existing networks with 3/spl times/3 SEs is an efficient and fast control algorithm that sets up a path between any source and destination pair. Instead of complex numerical calculations, the network can easily generate a primary routing tag and alternate tags through simple binary operations. Also, the network has a lot of favorable features, including regularity, symmetry, and easy rerouting capability under faults and conflicts. It is shown that at least two totally disjoint paths exist between any source and destination pair, which increase the degree of fault-tolerance. A deterministic permutation routing algorithm is also developed for the 8/spl times/8 composite banyan network, Using a simple tabular method, it is shown that the algorithm always finds a set of conflict-free tags.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

A new distribution network based on controlled switching elements and its applications

The paper presents a new distribution network which is capable of concentrating and shifting the incoming active packets simultaneously, without requiring dummy destination address generation and extraction processes. It has the structure of a reverse banyan network (RBN) and consists of controlled switching elements (CSEs) which is obtained by extending the passive iterative-cells introduced by Narasimha [1994]. The CSE-based RBN has a set of external control inputs (ECIs) in addition to the data input and output lines and can generate different output patterns according to the ECI values. It is shown through four properties that the CSE-based RBN can perform the distribution function of the conventional distributor. In addition, it is rigorously described in the properties how to determine the set of ECI values to achieve the desired distribution function, which includes the distribution in the normal mode, in the reversed mode, and in alternation of these two modes. The proposed CSE-based distributor can be applied to a variety of occasions by modifying the use of the counter, the numbers to write on the registers, and the table to store the ECI values. Some of useful examples are demonstrated through applications to shift-sequence permutation, N/spl times/R concentration, nonblocking point-to-point switching, and virtual FIFO queueing.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Modified composite Banyan network with an enhanced terminal reliability

The composite Banyan network orginally proposed earlier 1 can be constructed by adopting the characteristics of both the Banyan and the reverse Banyan networks. It has many interesting properties, such as a regular structure, tag-routing scheme, easy manipulation of alternate tags, etc. However, when n(=log 2 N) is even (where N is the number of terminals), the links between the two centre stages are duplicated. This is not desirable from the standpoint of switch faults. To overcome this problem we propose a modification of the original network. The modification scheme has been simplified to maintain most of the novel characteristics of the composite Banyan network. We show that the modified network has more internal paths between some source and destination pairs than the original network. These internal paths help to improve the network's terminal reliability. Using simulation, we verify that the modified network enhances terminal reliability.

Comments on "Nonblocking property of reverse banyan networks"

It is shown that the nonblocking property of reverse banyan networks mentioned in the above paper follows directly from the fact that banyan networks can realize permutations characterized by bitonic sequences.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Nonblocking property of reverse banyan networks

The authors present a new nonblocking property of the reverse banyan network under a particular input packet pattern at the input ports. The reverse banyan network is the mirror image of the banyan network. If the input packets of the N*N reverse banyan network have consecutive output address as modulo N, then the reverse banyan network is nonblocking. The routing of packets in the reverse banyan network is described, and the nonblocking property of the reverse banyan network is proved. A possible application of this property in the switching network is discussed. >