The board members are responsible for day-to-day management of the research unit throughout the university.

## Australian Professorial Fellow - Mathematics

### Research Interests

- Computational complexity theory and parameterized / multivariate complexity theory, foundations and methods
*Computer Science Unplugged ... online activities and games for all ages*, 231 pp., 1996, with Tim Bell and Ian Witten*Parameterized Complexity*, 530 pp., Springer-Verlag, 1999, with R.G. Downey

### Current research projects

- Applications of parameterized complexity and algorithms in computational social choice
- Foundations of fully multivariate complexity analysis
- Applications of parameterized complexity in cryptography and algebraic problems
- FPT metatheorems based on well-quasi-ordering

## Professorial Research Fellow - Mathematics

### Research Interests

- Computational complexity theory and parameterized / multivariate complexity theory, kernelization, combinatorial algorithms
- Applications of combinatorial algorithms in voting, election and consensus problems, and in computational biology, medical- and bio-informatics

### Current research projects

- Applications of parameterized complexity and algorithms to problems in computational social choice
- Foundations of multivariate complexity

## Senior Lecturer

### Research Interests

- Parameterized/multivariate (FPT) algorithms and algorithmic methods - Multivariate algorithms offer solutions to many problem that are intractable using the conventional algorithmic paradigm. Multivariate algorithmic techniques have so far proven useful in areas such as bioinformatics. Applications for FPT algorithms of particular interest are econometrics and analysis of social networking.
- Predictive analytics and data mining - Predictive analytics combines business intelligence with recent statistical techniques. This research combines this with recent advances in clustering and pattern searching using FPT techniques.
- Infectious disease control using mobile phone technology and cryptographic techniques Combinatorial Algorithms

### Current research projects

- Applications of parameterized complexity and algorithms in computational social choice
- Foundations of fully multivariate complexity analysis
- Applications of parameterized complexity in cryptography and algebraic problems
- FPT metatheorems based on well-quasi-ordering

**Parameterized complexity in algorithmic game theory**

The modern mathematical treatment of the study of decisions taken by participants whose interests are in conflict is now generally labeled as "game theory". To understand these interactions the theory provides some solution concepts. An important such a concept is the notion of Nash equilibrium, which provides a way of predicting the behavior of strategic participants in situations of conflicts. However, many decision problems regarding to the computation of Nash equilibrium are computationally hard problems. Motivated by these hardness results, we study the parameterized complexity of the Nash equilibrium. In parameterized complexity one considers computational problems in a two dimensional setting: the first dimension is the usual input size n, the second dimension is a positive integer k, the parameter. A problem is fixed-parameter tractable (FPT) if it can be solved in time f(k)n^(O(1)) where f denotes a computable, possibly exponential, function.

## Research expertise

- Algorithm and complexity
- Parameterized complexity
- Graph algorithms and Algorithmic game theory
- Combinatorial algorithm

## PhD (Mathematics)2010, Monash University

Thesis: "Transversals, Indivisible Plexes and Partitions of Latin Squares"

### Research Interests

- Parameterized complexity, structural graph theory, well-quasi-ordering.
- Combinatorics, combinatorial structures and designs, theory of Latin squares, algebra, finite sets, graph colourings.
- Combinatorial algorithms and applications in HPC

### Current research projects

- Infinite families of Latin squares with interesting properties.
- Algorithms for searching Latin squares, maximal sets of orthogonal Latin squares.
- Interactive programs for mathematical research and research communication.
- Graph orders, minor ideals, operators on minor ideals, algorithmic implications.
- Incremental problems in parameterized complexity.