Related papers: String Diagram of Optimal Transports
We present a study of the application of a variant of a recently introduced heuristic algorithm for the optimization of transport routes on complex networks to the problem of finding the optimal routes of communication between nodes on…
We develop a novel theoretical framework for understating OT schemes respecting a class structure. For this purpose, we propose a convex OT program with a sum-of-norms regularization term, which provably recovers the underlying class…
Network alignment, which aims to find node correspondence across different networks, is the cornerstone of various downstream multi-network and Web mining tasks. Most of the embedding-based methods indirectly model cross-network node…
Transformers have achieved state-of-the-art performance in numerous tasks. In this paper, we propose a continuous-time formulation of transformers. Specifically, we consider a dynamical system whose governing equation is parametrized by…
Optimal transport (OT) has become exceedingly popular in machine learning, data science, and computer vision. The core assumption in the OT problem is the equal total amount of mass in source and target measures, which limits its…
We present an iterative method to efficiently solve the optimal transportation problem for a class of strictly convex costs which includes quadratic and p-power costs. Given two probability measures supported on a discrete grid with n…
Branched Optimal Transport (BOT) is a generalization of optimal transport in which transportation costs along an edge are subadditive. This subadditivity models an increase in transport efficiency when shipping mass along the same route,…
Platooning represents an advanced driving technology designed to assist drivers in traffic convoys of varying lengths, enhancing road safety, reducing driver fatigue, and improving fuel efficiency. Sophisticated automated driving assistance…
Coordinating agents through hazardous environments, such as aid-delivering drones navigating conflict zones or field robots traversing deployment areas filled with obstacles, poses fundamental planning challenges. We introduce and analyze…
In many applications such as color image processing, data has more than one piece of information associated with each spatial coordinate, and in such cases the classical optimal mass transport (OMT) must be generalized to handle…
In this paper we report a new promising idea on the design and manufacturing of ply composite structures, tailored to exhibit maximum stiffness under given weight constraints and loading conditions. It is based on the idea behind an…
Optimal transport (OT) is a framework that can guide the design of efficient resource allocation strategies in a network of multiple sources and targets. This paper applies discrete OT to a swarm of UAVs in a novel way to achieve…
Motivated by an emerging framework of Autonomous Modular Vehicles, we consider the abstract problem of optimally routing two modules, i.e., vehicles that can attach to or detach from each other in motion on a graph. The modules' objective…
We study the estimation of optimal transport (OT) maps between an arbitrary source probability measure and a log-concave target probability measure. Our contributions are twofold. First, we propose a new evolution equation in the set of…
In this note, we generalize the classical optimal partial transport (OPT) problem by modifying the mass destruction/creation term to function-based terms, introducing what we term ``generalized optimal partial transport'' problems. We then…
In this work, we construct a novel numerical method for solving the multi-marginal optimal transport problems with Coulomb cost. This type of optimal transport problems arises in quantum physics and plays an important role in understanding…
We present an innovative framework for traffic dynamics analysis using High-Order Evolving Graphs, designed to improve spatio-temporal representations in autonomous driving contexts. Our approach constructs temporal bidirectional bipartite…
The classical problem of optimal transportation can be formulated as a linear optimization problem on a convex domain: among all joint measures with fixed marginals find the optimal one, where optimality is measured against a cost function.…
Optimal transport has become part of the standard quantitative economics toolbox. It is the framework of choice to describe models of matching with transfers, but beyond that, it allows to: extend quantile regression; identify discrete…
Tiering is an essential technique for building large-scale information retrieval systems. While the selection of documents for high priority tiers critically impacts the efficiency of tiering, past work focuses on optimizing it with respect…