Analysis of the structure of latin squares. The benefits to Australia of fundamental research in core disciplines such as mathematics are well documented. Discrete mathematics and combinatorics are boom disciplines of the computer age and this project seeks new knowledge concerning basic building blocks of combinatorial mathematics. The outcomes will be of interest to theoretical discrete mathematicians around the world, enhancing Australia's already high research profile in this important area ....Analysis of the structure of latin squares. The benefits to Australia of fundamental research in core disciplines such as mathematics are well documented. Discrete mathematics and combinatorics are boom disciplines of the computer age and this project seeks new knowledge concerning basic building blocks of combinatorial mathematics. The outcomes will be of interest to theoretical discrete mathematicians around the world, enhancing Australia's already high research profile in this important area of pure mathematical research. Importantly, the problems under investigation offer substantial opportunity for excellent postgraduate training, critical for the future of Australian research. Read moreRead less
Multivariate Algorithmics: Meeting the Challenge of Real World computational complexity. This Project will result in better methods for designing the algorithms that all computer applications depend on. Algorithms are the instruction sets that tell computers how to process information. Some information processing tasks are intrinsically difficult, even for computers working at enormous speeds. This Project will deliver new mathematical approaches to overcome these difficulties. More efficient al ....Multivariate Algorithmics: Meeting the Challenge of Real World computational complexity. This Project will result in better methods for designing the algorithms that all computer applications depend on. Algorithms are the instruction sets that tell computers how to process information. Some information processing tasks are intrinsically difficult, even for computers working at enormous speeds. This Project will deliver new mathematical approaches to overcome these difficulties. More efficient algorithmic approaches for difficult problems enable advances in all areas of computer applications such as medical diagnosis and health prediction, national security, communications efficiency, industrial productivity and all fields of science and engineering.Read moreRead less
Local reoptimization for turbocharging heuristics. Theoretical computer science has up until now had little impact on the design of effective heuristics. While data sets may be large, significant structure is almost always present and important to take into account when designing algorithms. Parameterised complexity considers the underlying structure by parameterising not only on the size of the input but also on structural parameters. This project aims to take advantage of the many opportunitie ....Local reoptimization for turbocharging heuristics. Theoretical computer science has up until now had little impact on the design of effective heuristics. While data sets may be large, significant structure is almost always present and important to take into account when designing algorithms. Parameterised complexity considers the underlying structure by parameterising not only on the size of the input but also on structural parameters. This project aims to take advantage of the many opportunities for new theories in the design of new heuristics and in turbocharging existing heuristics for computationally hard problems.Read moreRead less
Density regulation as a major determinant of population persistence: advancing empirical and theoretical approaches to conserve biodiversity. Without efficient application of limited conservation resources, more species will go extinct and invasive species will continue to proliferate. With a better understanding of extinction processes, a higher benefit:cost ratio will ensure better outcomes for biodiversity. We will directly address (1) the sustainable use of Australia's biodiversity by provid ....Density regulation as a major determinant of population persistence: advancing empirical and theoretical approaches to conserve biodiversity. Without efficient application of limited conservation resources, more species will go extinct and invasive species will continue to proliferate. With a better understanding of extinction processes, a higher benefit:cost ratio will ensure better outcomes for biodiversity. We will directly address (1) the sustainable use of Australia's biodiversity by providing evidence-based support for minimum viable population size targets to avoid extinction; (2) responding to climate change by determining the species- and environmentally specific contexts leading to elevated risks of extinction; and (3) protecting Australia from invasive diseases and pests by determining density targets that maximise eradication success.Read moreRead less