We investigate the fundamental aspects of computation, and how, through mathematically grounded modelling, they inform the design of efficient algorithmic solutions for real-world applications.
Our research spans three strengths across multidisciplinary research
We study the fundamental principles underlying the design, analysis, and optimisation of algorithms for solving computational problems efficiently and reliably. We combine mathematical rigour with practical applications to understand the limits of computation, data processing, and decision making. Central research areas include: computational geometry, which studies algorithms for spatial data and geometric structures; graph algorithms, which focus on networks, connectivity, routing, and matching; large-scale optimisation problems, which play a key role in developing methods that identify the best possible solutions under complex constraints, with applications ranging from logistics and scheduling to machine learning and data science; and sublinear-time algorithms, which investigate how useful approximations and insights can be obtained by examining only a small portion of massive datasets, enabling scalable solutions for modern data-intensive environments.
Together, these areas form the theoretical foundation for advances in computing, artificial intelligence, robotics, and networked systems. Their applications span autonomous vehicles, geographic information systems, communication networks, cybersecurity, bioinformatics, and large-scale data analytics. Algorithmic advances also support real-time decision making in areas such as transport, finance, healthcare, and environmental modelling.
Senior Lecturer Clément Canonne, Associate Professor Lijun Chang, Emeritus Professor Peter Eades, Professor Vincent Gramoli, Professor Joachim Gudmundsson, Professor Seokhee Hong, Associate Professor Joseph Lizier, Associate Professor Julian Mestre, Professor Mikhail Prokopenko, Senior Lecturer André van Renssen, Senior Lecturer Sasha Rubin, Associate Professor Qiang Tang, Lecturer Sri AravindaKrishnan Thyagarajan, Associate Professor Jiangshan Yu
In the course of our work, one of the central tools we draw on is computational complexity, in other words, the mathematical theory whose aim is to understand the inherent computational difficulty of problems, and the resources required to solve them. This includes classic resources such as; time, memory, and randomness, as well as measures of communication and interaction.
This work cuts across all subthemes and guides the design of algorithms and protocols by clarifying what is feasible and what is inherently hard. Computational complexity guides algorithm designers, and enables more reliable and efficient computing across modern digital infrastructures, including cryptography, distributed systems, and data science.
Senior Lecturer Clément Canonne, Professor Joachim Gudmundsson, Associate Professor Julian Mestre, Professor Mikhail Prokopenko, Senior Lecturer André van Renssen, Senior Lecturer Sasha Rubin, Associate Professor Qiang Tang, Lecturer Sri AravindaKrishnan Thyagarajan
We study the theoretical foundations of distributed computing: how multiple computing entities coordinate, communicate, and reach decisions reliably in the presence of failures, adversarial behaviour, and large-scale decentralisation.
Our research combines rigorous mathematical analysis to understand the fundamental limits of distributed coordination and to develop distributed algorithms that are provably correct, scalable, communication-efficient, and resilient. Our core research areas include; distributed consensus, fault tolerance, network disruptions and malicious attacks, and distributed optimisation and machine learning. A major focus of our work is secure distributed algorithms, which guarantee safety, privacy, and trust in open and adversarial environments.
Advances in this area underpin cloud computing, federated learning, financial technologies, blockchain networks, autonomous systems, telecommunications, and critical infrastructure such as energy grids and healthcare platforms. As society increasingly depends on interconnected systems, these advances directly support digital sovereignty, cybersecurity, and the safe deployment of large-scale intelligent systems. By developing new theories and algorithms for consensus, fault tolerance, and decentralised trust, we address fundamental challenges in how societies store information, exchange value, and access critical services.
Senior Lecturer Clément Canonne, Professor Vincent Gramoli, Associate Professor Qiang Tang, Lecturer Sri AravindaKrishnan Thyagarajan, Associate Professor Jiangshan Yu
We develop approaches to formally specify, verify, and synthesize digital systems, in order to ensure they behave as intended. This includes model checking which can systematically explore system executions, automated theorem proving which explores the space of logical proofs, and synthesis which constructs systems that meet formal requirements by design. Our work spans theoretical foundations of logic and automata, to applied domains such as verification of consensus, security, and blockchain protocols.
Our work advances the development of trustworthy digital systems by providing rigorous methods to guarantee correctness, security, and reliability. Formal methods are critical for decentralised technologies such as blockchain and consensus protocols, as well as for safety-critical systems in domains like autonomous systems and infrastructure. Overall, our research supports more secure software, resilient distributed platforms, and higher assurance in systems that underpin modern digital society.
Senior Lecturer Sasha Rubin, Associate Professor Qiang Tang, Lecturer Sri AravindaKrishnan Thyagarajan, Associate Professor Jiangshan Yu
Graph drawing studies the construction of geometric representations of graphs that are human-readable, interpretable, and analytically effective. The research seeks to balance aesthetic quality, structural fidelity, and computational efficiency, forming a core component of modern visual analytics and data mining systems. In particular, we investigate new models and characterisations of beyond-planar graphs, examining their combinatorial and structural properties, computational complexity, and algorithmic implications to support a broad range of applications, including financial market surveillance, fraud detection, bioinformatics, software engineering, communication networks, and counter-terrorism analysis.
Mathematically grounded and computationally efficient network visualisation algorithms will enable analysts to more accurately perceive the ground truth structure of large and complex datasets. The outcomes will support critical applications in security analysis, systems biology, financial monitoring, and large-scale software engineering. More broadly, these advances will provide a foundational framework for the next generation of trustworthy, scalable, and industry-ready visual analytics tools.
Associate Professor Lijun Chang, Emeritus Professor Peter Eades, Professor Seokhee Hong
We design and analyse principled and mathematically grounded algorithmic approaches to ensure the privacy and confidentiality of datasets. This includes, for instance, differential privacy and its variants, which provide strong guarantees on the privacy leakage when running algorithms on sensitive data, while preserving accuracy and quality of the results; as well as Zero-Knowledge proofs and arguments, which reveal only the desired output of the computation, and provably nothing else beyond the actual output.
By designing and analysing trusted approaches to privacy, our research enables trust and accountability for industries and sectors handling sensitive data, in areas as diverse as healthcare, the public sector, banks and the financial sector, and recommendation systems at large.
Senior Lecturer Clément Canonne, Associate Professor Qiang Tang, Lecturer Sri AravindaKrishnan Thyagarajan, Associate Professor Jiangshan Yu
We investigate the fundamental capabilities and limits of quantum computation. Specifically, we design new algorithms that leverage quantum phenomena to solve computational tasks more efficiently than via any known classical algorithm, or to achieve functionalities deemed impossible in the classical world. A key focus of our work is identifying the precise conditions required to achieve this "quantum advantage." This includes exploiting quantum mechanics for provable gains in data analysis and cryptography, as well as, on the flip side, developing classical cryptographic techniques provably resilient to attackers with quantum computing power (i.e., post-quantum cryptography).
By building our advances in quantum computing on rigorous foundations, designing and mapping out new emerging capabilities, our research not only provides a roadmap towards a quantum-enabled future: it also provides industry and government entities with a clear view of what gains and opportunities to expect and draw on, and the means to do so.
Senior Lecturer Clément Canonne, Associate Professor Qiang Tang, Lecturer Sri AravindaKrishnan Thyagarajan
For more information, please contact scs.theory@sydney.edu.au
