Related papers: Transport multi-paths with capacity constraints
This paper focuses on martingale optimal transport problems when the martingales are assumed to have bounded quadratic variation. First, we give a result that characterizes the existence of a probability measure satisfying some convex…
In this paper, we propose a model for evaluating the transmission performance of multipath transport. Previous researches focused exclusively on single pair users in simple scenarios. The distinct perspective in this paper is to build…
The branched transport problem, a popular recent variant of optimal transport, is a non-convex and non-smooth variational problem on Radon measures. The so-called urban planning problem, on the contrary, is a shape optimization problem that…
This paper connects discrete optimal transport to a certain class of multi-objective optimization problems. In both settings, the decision variables can be organized into a matrix. In the multi-objective problem, the notion of Pareto…
We propose a protocol optimization technique that is applicable to both weighted or unweighted graphs. Our aim is to explore by how much a small variation around the Shortest Path or Optimal Path protocols can enhance protocol performance.…
Traffic congestion is one of the major challenges faced by the transportation industry. While this problem carries a high economical and environmental cost, the need for an efficient design of optimal paths for passengers in multilayer…
We study the entropic regularizations of optimal transport problems under suitable summability assumptions on the point-wise transport cost. These summability assumptions already appear in the literature. However, we show that the weakest…
Capacity constrained optimal transport is a variant of optimal transport, which adds extra constraints on the set of feasible couplings in the original optimal transport problem to limit the mass transported between each pair of source and…
Many situations in physics, biology, and engineering consist of the transport of some physical quantity through a network of narrow channels. The ability of a network to transport such a quantity in every direction can be described by the…
We consider a vehicle routing problem which seeks to minimize cost subject to service level constraints on several groups of deliveries. This problem captures some essential challenges faced by a logistics provider which operates…
Our current world is revolutionned by the networks which are interconnecting any machine to any other one. Nowadays equipments are plugged to the network by the way of many different network adapters (Ethernet, wifi, GSM), and network…
We develop a new framework for branched transport between probability measures which are allowed to vary in time. This framework can be used to model problems where the underlying transportation network displays a branched structure, but…
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,…
We show that the capacity of a complex network that models a city street grid to support congested traffic can be optimized by using routes that collectively minimize the maximum ratio of betweenness to capacity in any link. Networks with a…
In this letter, we consider a transportation network with a 100\% penetration rate of connected and automated vehicles (CAVs) and present an optimal routing approach that takes into account the efficiency achieved in the network by…
In the classical Monge-Kantorovich problem, the transportation cost only depends on the amount of mass sent from sources to destinations and not on the paths followed by this mass. Thus, it does not allow for congestion effects. Using the…
The optimal transport problem studies how to transport one measure to another in the most cost-effective way and has wide range of applications from economics to machine learning. In this paper, we introduce and study an information…
We consider an optimal transportation problem with more than two marginals. We use a family of semi-Riemannian metrics derived from the mixed, second order partial derivatives of the cost function to provide upper bounds for the dimension…
Optimal transport is a framework for comparing measures whereby a cost is incurred for transporting one measure to another. Recent works have aimed to improve optimal transport plans through the introduction of various forms of structure.…
The question of which costs admit unique optimizers in the Monge-Kantorovich problem of optimal transportation between arbitrary probability densities is investigated. For smooth costs and densities on compact manifolds, the only known…