Graph Drawing and Network Visualization
Graph drawing focuses on finding geometric representations of graphs. Aside from theoretical interest, graph drawing is used in vast varieties of practical applications such as VLSI circuit layout, social network analysis, software system visualization, geometric routing, and bioinformatics. We examine theoretical bounds on the drawing aesthetics, and develop algorithms to draw graphs satisfying the constraints that arise from practical applications.
Computational Geometry
Computational geometry is concerned with the design and analysis of algorithms for solving geometric problems. Geometric problems arise from a variety of theoretical and applied fields, e.g., robot motion planning, database search, spatial data handling, computer graphics, etc. We develop efficient algorithms to solve such geometric problems and analyze their efficiency using discrete mathematical methods.
Visual Analytics of Big Data
Our lives today are deeply influenced by information technology which exposes us to a massive volume of data. Visualization is a powerful technique to deal with such large information. A good visualization can reveal the key properties of the data, as well as it helps users to make better decisions. We examine how to develop a visualization summary of large data to reveal interesting structures and features of the underlying information.
Graphs and Combinatorics
Graphs are widely used to represent a variety of relational data. Many computational problems are routinely solved using graph models both in theory and practice. We examine graph structures that satisfy a set of given constraints, and combinatorial problems on graphs such as enumeration and coloring.
Interdisciplinary research
The tools and techniques for solving geometric and graph theoretical problems can be applied effectively in many other research areas. We are particularly interested in applying these concepts, and theories to software testing and computer vision.
Global Water Future
Visual analytics can reveal important insight into large data. In a project of Global Water future, we are intograting visual analytics to analyze the change in cimate and water quality. Our water is at risk. In Canada and globally, we are facing unprecedented water-related challenges. Canada has some of the world's highest rates of warming, which impacts infrastructure, institutions, ecosystems and human health. Global Water Futures is finding solutions to those water threats in an era of global change.