Optimal Rearrangeable Multistage Connecting Networks

Abstract

A rearrangeable connecting network is one whose permitted states realize every assignment of inlets to outlets—that is, one in which it is possible to rearrange existing calls so as to put in any new call. In the effort to provide adequate telephone service with efficient networks it is of interest to be able to select rearrangeable networks (from suitable classes) having a minimum number of crosspoints. This problem is fully resolved for the class of connecting networks built of stages of identical square switches arranged symmetrically around a center stage: roughly, the optimal network should have as many stages as possible, with switches that are as small as possible, the largest switches being in the center stage; the cost (in crosspoints per inlet) of an optimal network of N inlets and N outlets is nearly twice the sum of the prime divisors of N, while the number of its stages is 2x — 1, where x is the number of prime divisors of N, in each case counted according to their multiplicity. By using a large number of stages, these designs achieve a far greater combinatorial efficiency than has been attained heretofore.

Perfectly Secure Multiparty Computation and the Computational Overhead of Cryptography

“…The main technical challenge is to perform "non-homogenous" computations on pairs of blocks, i.e., ones that are different from coordinate-wise addition or multiplication of blocks. We address this challenge by embedding the computation in a special form of a universal circuit based on the so-called Beneš network [5,29]. The high level idea is that the structure of the circuit reduces the computation in a given layer of the circuit to an arbitrary permutation between blocks (which can be done locally), homogenous operations, and a logarithmic number of distinct permutations within blocks.…”

“…This subcircuit can be made very regular using permutation networks as described by Waksman [29]. These are based on Beneš networks [5]. It follows from the construction that C only contains addition, multiplication and h-gates, where h swaps two input values x, y or leaves them alone, depending on a control-bit c:…”

Low-Complexity Multi-size Cyclic-Shifter for QC-LDPC Codes

“…To support various sizes, two barrel rotators are placed in parallel [4], [6] or series [7]. The other kind is based on a Benes network, which can route any N × N permutation [8], [9]. A Benes network is efficient for permutation but inappropriate for optimization with rotation properties.…”

WDM optical switching networks using sparse crossbars

“…The values of n and r satisfy that nr = Nk, and the value of m depends on the type of the overall optical switching network. For a permutation WDM optical switching network, m ≥ n [16]; and for a multicast WDM optical switching network, m ≥ 3(n − 1) log r log log r [17]. A three-stage Nk × Nk crossconnect under the fiberlink-based model is similar to that under the wavelengthbased model, except the first stage consists of inputindistinguishable sparse crossbars, which are shown in Fig.…”

“…Proof. The permutation and multicast capabilities can be easily verified for a WDM optical switching network under wavelength-based model by using Theorem 2, Theorem 3, and [16], [17].…”