Hypergraph models for complex discrete systems. This project aims to better understand the structure and properties of very large hypergraphs of various kinds. Hypergraphs are very general mathematical objects which can be used to model complex discrete systems. They arise naturally in many areas such as ecology, chemistry and computer science. Despite this, our theoretical understanding of very large, or random, hypergraphs lags far behind the intensely-studied special case of graphs. This proj ....Hypergraph models for complex discrete systems. This project aims to better understand the structure and properties of very large hypergraphs of various kinds. Hypergraphs are very general mathematical objects which can be used to model complex discrete systems. They arise naturally in many areas such as ecology, chemistry and computer science. Despite this, our theoretical understanding of very large, or random, hypergraphs lags far behind the intensely-studied special case of graphs. This project will answer many fundamental questions about large, random hypergraphs. The expected outcomes of the project also include new tools for working with hypergraphs, such as efficient algorithms for sampling hypergraphs. These outcomes will benefit researchers who use hypergraphs in their work and will enhance Australia's reputation for research in this area.Read moreRead less
A new model for random discrete structures: distributions, counting and sampling. Random discrete structures are used in countless applications across science for modelling complex systems. This project will study a new, very general model of random discrete structures which encapsulates both random networks and random matrices. This project will develop general tools for working with this model, thereby unlocking the model for use by practitioners in areas such as physics, biology, statistics a ....A new model for random discrete structures: distributions, counting and sampling. Random discrete structures are used in countless applications across science for modelling complex systems. This project will study a new, very general model of random discrete structures which encapsulates both random networks and random matrices. This project will develop general tools for working with this model, thereby unlocking the model for use by practitioners in areas such as physics, biology, statistics and cryptography. The questions that will be tackled are fundamental problems in probability, and include as special cases the analysis of subgraph distribution in models of random networks, and the joint distribution of entries of contingency tables, which are important in statistics.Read moreRead less
Discovery Early Career Researcher Award - Grant ID: DE120100049
Funder
Australian Research Council
Funding Amount
$375,000.00
Summary
New integer programming based theory, formulations and decomposition techniques with applications to integrated problems. Optimisation problems permeate science and industry. By developing new techniques to solve larger and harder problems than is currently possible, more complex questions can be answered, and more accurate solutions obtained. Industries can use such tools to make better financial, resource management, operational, and/or strategic planning decisions.
Discovery Early Career Researcher Award - Grant ID: DE140100708
Funder
Australian Research Council
Funding Amount
$297,003.00
Summary
Morphing graph drawings. A morphing is a continuous transformation between two drawings of the same topological graph such that at every time instant the drawing has the same topology. Morphings of graph drawings find applications in several areas of computer science, including computer graphics, animation, and modelling. This project will design algorithms for constructing morphings between graph drawings. Unlike any existing method to morph graph drawings, the algorithms designed for this proj ....Morphing graph drawings. A morphing is a continuous transformation between two drawings of the same topological graph such that at every time instant the drawing has the same topology. Morphings of graph drawings find applications in several areas of computer science, including computer graphics, animation, and modelling. This project will design algorithms for constructing morphings between graph drawings. Unlike any existing method to morph graph drawings, the algorithms designed for this project will guarantee bounds on the complexity of the vertex trajectories, guarantee bounds on the resolution of the drawing at every time instant, and deal with topological graphs that are not necessarily planar.Read moreRead less
Discovery Early Career Researcher Award - Grant ID: DE170100234
Funder
Australian Research Council
Funding Amount
$360,000.00
Summary
Exact and hybrid algorithms for the Aircraft Landing Problem. This project aims to develop algorithms with superior guaranteed performance. Aircraft Landing Problems (ALP) are an important class of decision problems. Optimal solution of an ALP is applicable in transportation and health care delivery, benefitting systems experiencing long delays. This project aims to address several of the Australian Government's Science and Research Priorities, focusing on food supply chains, effective operation ....Exact and hybrid algorithms for the Aircraft Landing Problem. This project aims to develop algorithms with superior guaranteed performance. Aircraft Landing Problems (ALP) are an important class of decision problems. Optimal solution of an ALP is applicable in transportation and health care delivery, benefitting systems experiencing long delays. This project aims to address several of the Australian Government's Science and Research Priorities, focusing on food supply chains, effective operation and resource allocation in transport, and better models of health care delivery and services.Read moreRead less
Discovery Early Career Researcher Award - Grant ID: DE150100720
Funder
Australian Research Council
Funding Amount
$375,000.00
Summary
Testing Isomorphism of Algebraic Structures. The algorithmic problem of isomorphism testing seeks to decide whether two objects from a mathematical category are essentially the same. This project focuses on the setting when the categories are from algebra, including but not limited to, groups and polynomials. It is a family of fundamental problems in complexity theory, with important applications in cryptography. The project aims to develop efficient algorithms with provable guarantee, or formal ....Testing Isomorphism of Algebraic Structures. The algorithmic problem of isomorphism testing seeks to decide whether two objects from a mathematical category are essentially the same. This project focuses on the setting when the categories are from algebra, including but not limited to, groups and polynomials. It is a family of fundamental problems in complexity theory, with important applications in cryptography. The project aims to develop efficient algorithms with provable guarantee, or formal hardness proofs, for these problems. Algorithms will be implemented to examine the impacts on certain cryptography schemes. The successful completion of this project will enhance the understanding of computational complexities of these problems, and identify the security of certain cryptography schemes.Read moreRead less
Discovery Early Career Researcher Award - Grant ID: DE190100888
Funder
Australian Research Council
Funding Amount
$333,924.00
Summary
Linear recurrence sequences over function fields and their applications. This project aims to deeply and systematically develop the theory of linear recurrence sequences (LRS) defined over function fields. Linear recurrence sequences (LRS) appear almost everywhere in mathematics and computer science. The project is expected to expand our knowledge on LRS and will span a wide range of new research directions. Through investigating and revealing the theoretical and practical aspects of LRS over fu ....Linear recurrence sequences over function fields and their applications. This project aims to deeply and systematically develop the theory of linear recurrence sequences (LRS) defined over function fields. Linear recurrence sequences (LRS) appear almost everywhere in mathematics and computer science. The project is expected to expand our knowledge on LRS and will span a wide range of new research directions. Through investigating and revealing the theoretical and practical aspects of LRS over function fields, the project will enrich the toolkits for cybersecurity by providing new approaches to cryptography. The outcomes of the project will help position Australia as a leader in this field.Read moreRead less
Extremal problems in hypergraph matchings. Matchings in hypergraphs are a way of understanding complex relationships between objects in any set. This project will develop a mathematical theory that covers both extreme and typical cases. This theory will have applications wherever hypergraphs are used as models, for example in machine learning, game theory, databases, data mining and optimisation.
Enumeration and properties of large discrete structures. This project aims to study a fundamental property of random graphs, by further developing a recently introduced approach to the problem of enumerating graphs with given degrees. Using this new method, the project expects to generate new knowledge on the number of connections that each node has with other nodes in a random graph, and to develop new strategies for counting the graphs or networks with a given property. The project expects to ....Enumeration and properties of large discrete structures. This project aims to study a fundamental property of random graphs, by further developing a recently introduced approach to the problem of enumerating graphs with given degrees. Using this new method, the project expects to generate new knowledge on the number of connections that each node has with other nodes in a random graph, and to develop new strategies for counting the graphs or networks with a given property. The project expects to produce new theoretical results as well as enhanced capabilities of mathematical research. Potential benefits arise through the uses of these theoretical combinatorial objects to study naturally occurring networks such as social networks, the network of the world wide web, and chemical compounds.Read moreRead less
Discovery Early Career Researcher Award - Grant ID: DE170100789
Funder
Australian Research Council
Funding Amount
$324,499.00
Summary
Advances in graph Ramsey theory. This project aims to solve significant questions at the forefront of graph Ramsey theory, which provides the theoretical background for understanding networks that are omnipresent in the modern world. Major progress is anticipated on the recently introduced concept of Ramsey equivalence, including the development of deep new tools that combine probabilistic methods, extremal graph theory and graph decomposition techniques. The project will use these new tools to ....Advances in graph Ramsey theory. This project aims to solve significant questions at the forefront of graph Ramsey theory, which provides the theoretical background for understanding networks that are omnipresent in the modern world. Major progress is anticipated on the recently introduced concept of Ramsey equivalence, including the development of deep new tools that combine probabilistic methods, extremal graph theory and graph decomposition techniques. The project will use these new tools to solve old questions on the structure of minimal Ramsey graphs, thus fostering the international competitiveness of Australian research and enhancing Australia's reputation as a knowledge nation.Read moreRead less