Towards an optimised VLSI design algorithm for the constant matrix multiplication problem

The efficient design of multiplierless implementations of constant matrix multipliers is challenged by the huge solution search spaces even for small scale problems. Previous approaches tend to use hill-climbing algorithms risking sub-optimal results. The proposed algorithm avoids this by exploring parallel solutions. The computational complexity is tackled by modelling the problem in a format amenable to genetic programming and hardware acceleration. Results show an improvement on state of the art algorithms with future potential for even greater savings

Fringe analysis for parallel MacroSplit insertion algorithms in 2--3 trees

We extend the fringe analysis (used to study the expected behavior of balanced search trees under sequential insertions) to deal with synchronous parallel insertions on 2--3 trees. Given an insertion of k keys in a tree with n nodes, the fringe evolves following a transition matrix whose coefficients take care of the precise form of the algorithm but does not depend on k or n. The derivation of this matrix uses the binomial transform recently developed by P. Poblete, J. Munro and Th. Papadakis. Due to the complexity of the preceding exact analysis, we develop also two approximations. A first one based on a simplified parallel model, and a second one based on the sequential model. These two approximated analysis prove that the parallel insertions case does not differ significantly from the sequential case, namely on the terms O(1/n^2).Postprint (published version

A Parallel Riccati Factorization Algorithm with Applications to Model Predictive Control

Model Predictive Control (MPC) is increasing in popularity in industry as more efficient algorithms for solving the related optimization problem are developed. The main computational bottle-neck in on-line MPC is often the computation of the search step direction, i.e. the Newton step, which is often done using generic sparsity exploiting algorithms or Riccati recursions. However, as parallel hardware is becoming increasingly popular the demand for efficient parallel algorithms for solving the Newton step is increasing. In this paper a tailored, non-iterative parallel algorithm for computing the Riccati factorization is presented. The algorithm exploits the special structure in the MPC problem, and when sufficiently many processing units are available, the complexity of the algorithm scales logarithmically in the prediction horizon. Computing the Newton step is the main computational bottle-neck in many MPC algorithms and the algorithm can significantly reduce the computation cost for popular state-of-the-art MPC algorithms