The Complexity of Computations by Networks

We survey the current state of knowledge concerning the computation of Boolean functions by networks, with particular emphasis on the addition and multiplication of binary numbers

Complexity of Computations with Matrices and Polynomials

We review the complexity of polynomial and matrix computations, as well as their various correlations to each other and some major techniques for the design of algebraic and numerical algorithms

Two-band fast Hartley transform

This article has been made available through the Brunel Open Access Publishing Fund.Efficient algorithms have been developed over the past 30 years for computing the forward and inverse discrete Hartley transforms (DHTs). These are similar to the fast Fourier transform (FFT) algorithms for computing the discrete Fourier transform (DFT). Most of these methods seek to minimise the complexity of computations and or the number of operations. A new approach for the computation of the radix-2 fast Hartley transform (FHT) is presented. The proposed algorithm, based on a two-band decomposition of the input data, possesses a very regular structure, avoids the input or out data shuffling, requires slightly less multiplications than the existing approaches, but increases the number of additions

A Lower Bound Technique for Communication in BSP

Communication is a major factor determining the performance of algorithms on current computing systems; it is therefore valuable to provide tight lower bounds on the communication complexity of computations. This paper presents a lower bound technique for the communication complexity in the bulk-synchronous parallel (BSP) model of a given class of DAG computations. The derived bound is expressed in terms of the switching potential of a DAG, that is, the number of permutations that the DAG can realize when viewed as a switching network. The proposed technique yields tight lower bounds for the fast Fourier transform (FFT), and for any sorting and permutation network. A stronger bound is also derived for the periodic balanced sorting network, by applying this technique to suitable subnetworks. Finally, we demonstrate that the switching potential captures communication requirements even in computational models different from BSP, such as the I/O model and the LPRAM

Computations on Nondeterministic Cellular Automata

The work is concerned with the trade-offs between the dimension and the time and space complexity of computations on nondeterministic cellular automata. It is proved, that 1). Every NCA \Cal A of dimension $r$, computing a predicate $P$ with time complexity T(n) and space complexity S(n) can be simulated by $r$-dimensional NCA with time and space complexity $O(T^{\frac{1}{r+1}} S^{\frac{r}{r+1}})$ and by $r+1$-dimensional NCA with time and space complexity $O(T^{1/2} +S)$. 2) For any predicate $P$ and integer $r>1$ if \Cal A is a fastest $r$-dimensional NCA computing $P$ with time complexity T(n) and space complexity S(n), then $T= O(S)$. 3). If $T_{r,P}$ is time complexity of a fastest $r$-dimensional NCA computing predicate $P$ then T_{r+1,P} &=O((T_{r,P})^{1-r/(r+1)^2}), T_{r-1,P} &=O((T_{r,P})^{1+2/r}). Similar problems for deterministic CA are discussed.Comment: 18 pages in AmsTex, 3 figures in PostScrip

Modelling the Duration of Multihop Paths in Mobile Ad Hoc Networks

Mobile ad hoc networks are characterized by having nodes that are cooperative and communicate without any kind of infrastructure. The mobility and multihop capability of these networks leads the network topology to change rapidly and unpredictably; this aspect must be incorporated in effective models to describe the dynamics of multihop paths.\newline When modeling the duration of multihop paths, a great part of the literature assumes that the links of multihop paths behave independently. This simplifies the modeling and reduces the complexity of computations. However, each link shares a common node with each of its neighbor links, turning the independent link assumption ge-nerally not valid. In this paper, we use a piecewise deterministic Markov model that characterizes the random behaviour of a multihop path not assuming independent links. We obtain the mean path duration of multihop paths and compare the results for the used model with the ones obtained by assuming independent links. Numerical results illustrate that independent link approximation results underestimate the mean path duration, with the most significant differences being observed with low node mobility and higher path durations

A Numerical Implementation of the Soret Effect in Drying Processes

Drying of porous media is strictly governed by heat and mass transfer. However, contrary to the definition that drying is simultaneous transport mechanisms of heat and mass, most past and current models either account for temperature or concentration gradient effects on drying. Even though the complexity of computations of these processes varies with area of application, in most cases, the Dufour and Soret effects are neglected. This leads to deviations and uncertainties on the assumptions and interpretations of these and other relevant effects on drying. This paper covers the theoretical methods to derive the coupled transfer effects. In addition, this work proposes and formulates relevant heat and mass transfer equations, as well as the governing equations for drying processes with Dufour and Soret effects. The application of a numerical approach to solve the equations allows for studying of the influence of these effects on the design and operation of dryers. It is shown that the Soret effect can be highly relevant on drying operations with dynamic heating operation. While for drying processes where the steady state drying process predominates, the effect is deemed negligible