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
Elliptic curves: number theoretic and cryptographic aspects. Smart information use is of fundamental nature and has a great number of applications. First-generation security solutions are unable to support the modern requirements and new security infrastructures are emerging that must be carefully, but rapidly, defined. This urgently needs new mathematical tools, which is the main goal of this project.
Beyond Planarity: Algorithms for Visualisation of Sparse Non-Planar Graphs. This project aims to develop new efficient algorithms to enable analysts to visually understand complex data and detect anomalies or patterns. It aims to develop visualisation algorithms for sparse non-planar graphs arising from real-world networks. Specifically, the project plans to investigate structural properties of sparse non-planar topological graphs such as k-planar graphs, k-skew graphs, and k-quasi-planar graphs ....Beyond Planarity: Algorithms for Visualisation of Sparse Non-Planar Graphs. This project aims to develop new efficient algorithms to enable analysts to visually understand complex data and detect anomalies or patterns. It aims to develop visualisation algorithms for sparse non-planar graphs arising from real-world networks. Specifically, the project plans to investigate structural properties of sparse non-planar topological graphs such as k-planar graphs, k-skew graphs, and k-quasi-planar graphs, and design efficient testing algorithms, embedding algorithms, and drawing algorithms. These algorithms will be evaluated with real-world social networks and biological networks. New insights into the mathematical interplay between combinatorial and geometric structures would provide a theoretical foundation for a new generation of complex network visualisation methods with potential applications in social networks, systems biology, health informatics, finance and security.Read moreRead less
Algorithms for hard graph problems based on auxiliary data. When solving computational problems, algorithms usually access only the data that is absolutely necessary to define the problem. However, much more data is often readily available. Especially for important or slowly evolving data, such as road networks, social graphs, company rankings, or molecules, more and more auxiliary data becomes available through computational processes, sensors, and simple user entries. This auxiliary data can g ....Algorithms for hard graph problems based on auxiliary data. When solving computational problems, algorithms usually access only the data that is absolutely necessary to define the problem. However, much more data is often readily available. Especially for important or slowly evolving data, such as road networks, social graphs, company rankings, or molecules, more and more auxiliary data becomes available through computational processes, sensors, and simple user entries. This auxiliary data can greatly speed up an algorithm and improve its accuracy. This project aims to design improved algorithms that harness auxiliary data to solve selected high-impact NP-hard graph problems, and will build a new empowering theory to discern when auxiliary data can be used to improve algorithms.Read moreRead less
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
Algorithmic engineering and complexity analysis of protocols for consensus. Opinions, rankings, observations, votes, gene sequences, sensor-networks in security systems or climate models. Massive datasets and the ability to share information at unprecedented speeds, makes finding the most central representative, the Consensus Problem, extremely complex. This research delivers new insights and new, efficient algorithms.
Efficient structure search over large graphs. The project aims to develop advanced search technology to support large-scale graph applications. The success of the project not only brings a breakthrough in technology development but also provides training for high quality personnel in this important and growing area, and brings considerable economic and social benefits to Australia.