NSF Award
2203278
Efficient methods of storing and querying large data volumes play a crucial role in a majority of computer applications. In many situations, both the stored data and the queries can be represented as geometric objects, such as points, lines, and rectangles. This scenario is traditionally studied in computational geometry. However, geometric data structures have numerous applications in other areas of Computer Science, from spatial databases to geographic information systems, from computer graphics to bioinformatics. This project will study geometric data structures and their connections with other areas of theoretical Computer Science. The investigator and his students will also study the implementations of obtained algorithms and their potential applications. <br/><br/><br/>This project will focus on fundamental geometric data structuring problems: the orthogonal range searching problem, the point location problem, the nearest neighbor problem, and the dynamic convex hull problem. Despite several decades of extensive study, there are still several important open questions related to these problems.<br/>This project aims to extend and deepen the knowledge of this area: reduce or eliminate the gaps between the lower and upper bounds, investigate the relative complexities of problems in different models of computation, and find more efficient ways to dynamize the static data structures. The investigator will also explore the connections between geometric data structures and algorithms in the external memory model, making the project's contributions applicable to a larger class of applications.<br/><br/>This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.
