The Algorithms Group focuses on designing and analysing algorithms that solve computational problems efficiently. Group members combine techniques from computer science, discrete mathematics, and probability theory in algorithms research spanning the following areas:
Theory of Bio-Inspired Algorithms covers general-purpose optimisation paradigms that draw inspiration from biological systems. Evolutionary algorithms mimic Darwinian principles such as survival of the fittest to artificially evolve candidate solutions for optimisation and design problems. Swarm intelligence paradigms such as ant colony optimisation or particle swarm optimisation are based on the collective intelligence of animal swarms. We work on providing a theoretical foundation for understanding the working principles of these heuristic algorithms through quantifying how quickly they find satisfactory solutions for various problems. This exposes how performance depends on algorithmic parameters and design choices, and helps to design better bio-inspired optimisation algorithms.
Numerical Algorithms: One of the most important problems in geometric modelling is the calculation of the points of intersection of curves and surfaces. Tangential points of intersection are of particular interest, but they are difficult to compute reliably because multiple roots of a polynomial are extremely sensitivity to noise. We use methods for the computation of multiple roots of polynomials to develop better methods for deblurring images because a blurred image is formed by the convolution of an exact image and a point spread function, and the product of two polynomials is formed by the convolution of their coefficients.