The vertex colouring problem (VCP) and its generalisations have myriad applications in computer networks. To solve the VCP with colours, numerous distributed algorithms based on LOCAL model have been proposed to reduce time complexity (the number of rounds), where is the maximum vertex degree in the graph. In this paper, the authors present a distributed algorithm based on modified LOCAL model (DIAMOND) that reduces the number of rounds to one. It greedily solves the VCP with at most colours. Computational results on Geometry (GEOM) graphs show that the number of used colours to colour each instance using DIAMOND is about . DIAMOND is easily extended to solve greedily generalised VCPs in only one round. Moreover, they present two efficient resource allocation algorithms using DIAMOND. They allocate more resource to the graph compared with -colouring and even to -colouring algorithms, where is the average vertex degree of the graph. They run in two and rounds.

In this study, a multi-agent coordination problem with steady-state regulation constraints is investigated for a class of non-linear systems. Unlike the existing leader-following coordination formulations, a reference signal is not given by a dynamic autonomous leader but determined as the optimal solution of a distributed optimisation problem. Furthermore, the authors consider a global constraint having noisy data observations for the optimisation problem, which implies that the reference signal is not trivially available with the existing optimisation algorithms. To handle these challenges, the authors present a passivity-based analysis and design approach by using only local objective function, local data observation and exchanged information from their neighbours. The proposed distributed algorithms are shown to achieve the optimal steady-state regulation by rejecting the unknown observation disturbances for passive non-linear agents, which are persuasive in various practical problems. Applications and simulation examples are then given to verify the effectiveness of the proposed design.

In this article, the authors study a leader-following consensus problem for multi-agent systems in a sampled-data setting. A distributed coordination algorithm based on sampled-data control is proposed to track the considered leader. By employing M-matrix theory, the authors derive sufficient conditions on the sampling period and control parameters to ensure that the tracking errors are bounded. Numerical simulations are presented to illustrate the effectiveness of the theoretical results. Moreover, some previous results concerning the leader-following problem with switched coupling topology are improved.

A number of parallel algorithms admit a static torus-structured task graph. Hexagonal honeycomb torus (HHT) networks are regarded as promising candidates for interconnection networks. In order to efficiently execute a torus-structured parallel algorithm on an HHT, it is essential to map the tasks to processors so that the communication overhead is minimised. The study proves that a (3n, 2n) torus can be embedded into an nth-order HHT with dilation 3, congestion 4, expansion 1 and load factor 1. Consequently, a parallel algorithm with a (3n, 2n) torus task graph can be executed on an nth-order HHT efficiently.

An algorithm for software or hardware implementation is presented, allowing fast computation of cyclic redundancy checks with arbitrary polynomials and a high flexibility, such as updating of checksums after modifying data block parts with a known old checksum.

A novel quasi-Newton algorithm for adaptively estimating the principal eigensubspace of a covariance matrix by making use of an approximation of its Hessian matrix is derived. A rigorous analysis of the convergence properties of the algorithm by using the stochastic approximation theory is presented. It is shown that the recursive least squares (RLS) technique can be used to implement the quasi-Newton algorithm, which significantly reduces the computational requirements from O( pN² ) to O( pN), where N is the data vector dimension and p is the number of desired eigenvectors. The algorithm is further generalised by introducing two adjustable parameters that efficiently accelerate the adaptation process. The proposed algorithm is applied to different applications such as eigenvector estimation and the Comon–Golub test in order to study the convergence behaviour of the algorithm when compared with others such as PASTd, NIC, and the Kang et al. quasi-Newton algorithm. Simulation results show that the new algorithm is robust against changes of the input scenarios and is thus well suited to parallel implementation with online deflation.

An AB² operation is known as an efficient basic operation for public key cryptosystems over GF(2^m), and various systolic arrays for performing AB² operations have already been proposed using a standard basis representation. However, these circuits have certain shortcomings for cryptographic application due to their high circuit complexity and long latency. Therefore, further research on an efficient AB² multiplication circuit is still needed. Accordingly, the authors present a new AB² algorithm and its systolic realisations in GF(2^m). First, a new algorithm is proposed based on the MSB-first scheme using a standard basis representation. Thereafter, bit-parallel and bit-serial systolic power multipliers are derived that exhibit a lower hardware complexity and smaller latency than conventional approaches. In addition, since the proposed architectures incorporate simplicity, regularity, modularity, and pipelinability, they are well suited to VLSI implementation and can be easily applied as a basic architecture for computing an inverse/division operation and in crypto-processor chip design.

It is well known that optimal control techniques can provide the ability to design suitable strategies, however, the on-line computing requirements are excessive. The normal procedure is to make various assumptions so that the processing demands are reduced. Based on these assumptions, sequences of linear-quadratic-performance optimal control problems need to be considered. These in turn give rise to standard two-point-boundary-value problems. The solution to such problems involves the computation of the algebraic Riccati equations (AREs). The block diagonal decomposition LDL^T, is the key step for those algorithms based on the matrix sign function that are used in solving the AREs. The last few years have witnessed a tremendous effort towards the development of reliable algorithms to solve the AREs and apply it in industrial situations. However, all the implementations and testing of the proposed algorithms have been performed on powerful machines thereby limiting their practical application. The authors present a pivoting strategy that: (i) requires only one-dimension of the matrix for the selection of the pivot; (ii) generates regular communication patterns; and (iii) establishes a software mechanism for the development of fault tolerant applications. The results obtained from a multiprocessor system with a one-way ring topology indicate that the block diagonal LDL^T decomposition is a true candidate for real-time use and fault tolerant applications and also as a framework-test for the LAPACK library.

A parallelised max-Log-MAP model (P-max-Log-MAP) that exploits the sub-word parallelism and very long instruction word architecture of a microprocessor or a digital signal processor (DSP) is presented. The proposed model reduces considerably the computational complexity of the max-Log-MAP algorithm; and therefore facilitates easy implementation.

A connection between a neurofuzzy network model with the Mixture of Experts Network (MEN) modelling approach is established. Based on this linkage, two new neurofuzzy MEN construction algorithms are proposed to overcome the curse of dimensionality that is inherent in the majority of associative memory networks and/or other rule based systems. The first construction algorithm employs a function selection manager module in an MEN system; a conventional latticed based neurofuzzy model is initially generated followed by parsimonious model selection at each iteration using a new simple MEN construction method using a cost criterion based on the MEN model output sensitivity to each expert. This scheme uses an extension to the well established normalised least means squares as a model parametric learning algorithm. The second construction algorithm is based on a new parallel learning algorithm in which each model rule is trained independently, for which the parameter convergence property of the new learning method is established. As with the first approach, an expert selection criterion is utilised in this algorithm, where each rule is either trained or inhibited. These two construction methods are equivalent in their effectiveness in overcoming the curse of dimensionality by reducing the dimensionality of the regression vector, but the latter has the additional computational advantage of parallel processing. The proposed algorithms are analysed for effectiveness followed by numerical examples to illustrate their efficacy for some difficult data based modelling problems.