AF: Small: Collaborative Research:Geometric and topological algorithms for analyzing road network data

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The project aims to develop theoretically grounded, effective methods for analyzing data associated with road networks -- using graphs that represent road networks as a framework for analyzing network data. Thanks to the spread of GPS-enabled devices, trajectory data has become ubiquitous. Many other sources, including census data and crime statistics, have addresses or geographic locations that link to an underlying road network. Algorithms with mathematical guarantees will be developed to align trajectories to the network under natural and realistic properties of true trajectories, to reconstruct road networks from trajectory and density data. It will also provide two frameworks for comparing data-endowed networks at different levels. While the problems of trajectory alignment, map reconstruction, and map comparison have attracted a lot of attention in the GIS community, most approaches are ad-hoc, provide no quality guarantees, and are limited to post-hoc analysis. This project will provide novel theoretical foundations combining approaches from computational topology and geometry, and will further advance the state-of-the-art of the field of topological / geometric data analysis. The PIs will continue to combine educational and research activities through this project. Students will be tightly integrated into the research and practical implementation of this project, and will be trained in integrating geometric thinking, algorithms development, and (trajectory) data analysis. The combination of such skills is increasingly important in data science. Topics involved in this project will enrich the course material and curriculum development at each of the three institutions.