Related papers: Formulation of branched transport as geometry opti…
Optimal Transport has received much attention in Machine Learning as it allows to compare probability distributions by exploiting the geometry of the underlying space. However, in its original formulation, solving this problem suffers from…
We investigate the problem of optimal transport in the so-called Beckmann form, i.e. given two Radon measures on a compact set, we seek an optimal flow field which is a vector valued Radon measure on the same set that describes a flow…
We investigate the problem of efficiently computing optimal transport (OT) distances, which is equivalent to the node-capacitated minimum cost maximum flow problem in a bipartite graph. We compare runtimes in computing OT distances on data…
Unbalanced optimal transport (UOT) provides a flexible way to match or compare nonnegative finite Radon measures. However, UOT requires a predefined ground transport cost, which may misrepresent the data's underlying geometry. Choosing such…
This note addresses computational difficulty of the Gromov-Wasserstein distance frequently mentioned in the literature. We provide details on the structure of the Gromov-Wasserstein distance optimization problem that show its non-convex…
Air pollution can be studied in the urban structure regulated by transport networks. Transport networks can be studied as geometric and topological graph characteristics through designed models. Current studies do not offer a comprehensive…
We introduce a general class of transport distances ${\rm WB}_{\Lambda}$ over the space of positive semi-definite matrix-valued Radon measures $\mathcal{M}(\Omega,\mathbb{S}_+^n)$, called the weighted Wasserstein-Bures distance. Such a…
Motivated by the shape of transportation networks such as subways, we consider a distribution of points in the plane and ask for the network $G$ of given length $L$ that is optimal in a certain sense. In the general model, the optimality…
Optimal maps, solutions to the optimal transportation problems, are completely determined by the corresponding c-convex potential functions. In this paper, we give simple sufficient conditions for a smooth function to be c-convex when the…
We prove existence of an optimal transport map in the Monge-Kantorovich problem associated to a cost $c(x,y)$ which is not finite everywhere, but coincides with $|x-y|^2$ if the displacement $y-x$ belongs to a given convex set $C$ and it is…
A key inequality which underpins the regularity theory of optimal transport for costs satisfying the Ma--Trudinger--Wang condition is the Pogorelov second derivative bound. This translates to an apriori interior $C^1$ estimate for smooth…
This paper introduces two variational formulations for a model of robust optimal transport, that is, the problem of designing optimal transport networks that are resilient to potential damages, balancing construction costs against the…
We propose a new approach to graph compression by appeal to optimal transport. The transport problem is seeded with prior information about node importance, attributes, and edges in the graph. The transport formulation can be setup for…
While motion planning approaches for automated driving often focus on safety and mathematical optimality with respect to technical parameters, they barely consider convenience, perceived safety for the passenger and comprehensibility for…
We introduce a new second order stochastic algorithm to estimate the entropically regularized optimal transport cost between two probability measures. The source measure can be arbitrary chosen, either absolutely continuous or discrete,…
The network structure of an urban transportation system has a significant impact on its traffic performance. This study uses network indicators along with several traffic performance measures including speed, trip length, travel time, and…
The goal of traffic management is efficiently utilizing network resources via adapting of source sending rates and routes selection. Traditionally, this problem is formulated into a utilization maximization problem. The single-path routing…
Urban form plays a crucial role in shaping transportation patterns, accessibility, energy consumption, and more. Our study examines the relationship between urban form and transportation energy use by developing a parametric model that…
Sliced Optimal Transport (SOT) is a rapidly developing branch of optimal transport (OT) that exploits the tractability of one-dimensional OT problems. By combining tools from OT, integral geometry, and computational statistics, SOT enables…
Optimal transport provides a metric which quantifies the dissimilarity between probability measures. For measures supported in discrete metric spaces, finding the optimal transport distance has cubic time complexity in the size of the…