A sparse algorithm for dense optimal transport

Discrete optimal transport solvers do not scale well on dense large problems since they do not explicitly exploit the geometric structure of the cost function. In analogy to continuous optimal transport we provide a framework to verify global optimality of a discrete transport plan locally. This allows construction of a new sparse algorithm to solve large dense problems by considering a sequence of sparse problems instead. Any existing discrete solver can be used as internal black-box. The case of noisy squared Euclidean distance is explicitly detailed. We observe a significant reduction of run-time and memory requirements.

• Type: Journal
• Year: 2015
• Where: SCALESPACE
• Authors: Bernhard Schmitzer
• Keywords: Computer Vision, SCALESPACE 2015