Project Grant 2223870

This three-year, $631,860 project grant from the National Science Foundation's Division of Computing and Communication Foundations, under the Computer and Information Science and Engineering program, will support the development of efficient algorithms for optimal transport in geometric settings. The researchers at Duke University will advance theoretical understanding of optimal transport and bridge gaps between theory and practice of algorithm development. They will exploit combinatorial, geometric, and statistical properties of optimal transport to design simple, scalable algorithms computing high-quality transport plans for discrete and continuous distributions over compact regions in Euclidean space. Emphasis will be placed on algorithms with good worst-case running times and better expected performance on stochastic inputs. The researchers will also explore techniques to address the curse of dimensionality in optimal transport of high-dimensional distributions and develop new algorithms for data analysis and quality assessment using optimal transport distances.