- Survivable networks
- Shortest network design
- Discrete and computational geometry
- Combinatorial optimisation
M. Brazil, M Volz, M Zachariasen, C. Ras, D Thomas. Computing minimum 2-edge-connected Steiner networks in the Euclidean plane. Networks, 2018. doi: 10.1002/net.21835.
M. Brazil, M Volz, M Zachariasen, C. Ras, D Thomas. New pruning rules for the Steiner tree problem and 2-connected Steiner network problem. Computational Geometry: Theory and Applications, 37-49, 2018. doi: 10.1016/j.comgeo.2018.10.003.
C. Ras, Konrad Swanepoel, Doreen Anne Thomas. Approximate Euclidean Steiner Trees. Journal of Optimization Theory and Applications, 172, 845-873, 2017. doi: 10.1007/s10957-016-1036-5.
Patrick J Andersen, C. Ras. Minimum Bottleneck Spanning Trees with Degree Bounds. Networks, 68, 302-314, 2016. doi: 10.1002/net.21710.
M Brazil, C. Ras, DA Thomas. An exact algorithm for the bottleneck 2-connected k-Steiner network problem in L-p planes. Discrete Applied Mathematics, 201, 47-69, 2016. doi: 10.1016/j.dam.2015.07.029.
My research primarily involves the use of techniques from graph theory, optimisation, and computational geometry for designing networks that are minimal under various edge-length objectives. I am interested in the design and asymptotic analysis of geometric network optimisation algorithms, including aspects such as computational complexity, fixed-parameter tractability, and NP-completeness. Some of the applications of my work are the optimisation of energy consumption in wireless ad-hoc networks, VLSI design, and phylogenetic tree construction. One of my current projects seeks to find mathematical tools and algorithms for the deployment and augmentation of optimal survivable networks. In this problem one is required to introduce a set of nodes and links into a geometric space so that the resultant network is multi-connected and is optimal with respect to some objective (for instance the sum of all edge-lengths). Finding good solutions to this problem will contribute to the economical construction of robust infrastructure and telecommunications networks, including transportation networks, utility networks, and fibre-optic networks such as the NBN.
Current Postgraduate Supervision
|Patrick ANDERSEN||"Coverage and connectivity in wireless sensor networks"|
Current MSc Students
Past MSc Students