Related papers: Dynamic Optimal Transport with optimal star shaped…
Many optimization problems can be naturally represented as (hyper) graphs, where vertices correspond to variables and edges to tasks, whose cost depends on the values of the adjacent variables. Capitalizing on the structure of the graph,…
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.…
We provide new results on the structure of optimal transportation networks obtained as minimizers of an energy cost functional consisting of a kinetic (pumping) and material (metabolic) cost terms, constrained by a local mass conservation…
Many problems in machine learning involve calculating correspondences between sets of objects, such as point clouds or images. Discrete optimal transport provides a natural and successful approach to such tasks whenever the two sets of…
We study the replacement paths problem in the $\mathsf{CONGEST}$ model of distributed computing. Given an $s$-$t$ shortest path $P$, the goal is to compute, for every edge $e$ in $P$, the shortest-path distance from $s$ to $t$ avoiding $e$.…
In this paper, we introduce a new model for sublinear algorithms called \emph{dynamic sketching}. In this model, the underlying data is partitioned into a large \emph{static} part and a small \emph{dynamic} part and the goal is to compute a…
Understanding the complex patterns in space-time exhibited by active systems has been the subject of much interest in recent times. Complementing this forward problem is the inverse problem of controlling active matter. Here we use optimal…
We introduce a novel model based on the discrete optimal transport problem that incorporates congestion costs and replaces traditional constraints with weighted penalization terms. This approach better captures real-world scenarios…
We introduce a new graph problem, the token dropping game, and we show how to solve it efficiently in a distributed setting. We use the token dropping game as a tool to design an efficient distributed algorithm for stable orientations and…
This paper discusses a graph based route solving algorithm to find the optimal path for an electric vehicle picking the best charging locations among thousands to minimize the total cumulative driving distance between the end points of the…
We study the urban-scale macroscopic traffic flow in city networks. Star graph is considered as traffic network. Star graphs with controlled traffic flow are transformed to various cell-transmission graphs by using the cell transmission…
We analyze several problems of Optimal Transport Theory in the setting of Ergodic Theory. In a certain class of problems we consider questions in Ergodic Transport which are generalizations of the ones in Ergodic Optimization. Another class…
In this paper we investigate the numerical approximation of an analogue of the Wasserstein distance for optimal transport on graphs that is defined via a discrete modification of the Benamou--Brenier formula. This approach involves the…
Optimal transport is widely used in pure and applied mathematics to find probabilistic solutions to hard combinatorial matching problems. We extend the Wasserstein metric and other elements of optimal transport from the matching of sets to…
Entropic regularization provides a generalization of the original optimal transport problem. It introduces a penalty term defined by the Kullback-Leibler divergence, making the problem more tractable via the celebrated Sinkhorn algorithm.…
This paper develops a comprehensive theory of optimal transport for signed (real) measures on Rd. Extending the classical Brenier theorem, we consider Jordan decompositions of measures with possibly fractal singular parts. Under suitable…
We present a 2-step optimal transport approach that performs a mapping from a source distribution to a target distribution. Here, the target has the particularity to present new classes not present in the source domain. The first step of…
We show in full generality the stability of optimal traffic paths in branched transport: namely we prove that any limit of optimal traffic paths is optimal as well. This solves an open problem in the field (cf. Open problem 1 in the book…
The Monge-Kantorovich transportation problem involves optimizing with respect to a given a cost function. Uniqueness is a fundamental open question about which little is known when the cost function is smooth and the landscapes containing…
We introduce a new variant of the weak optimal transport problem where mass is distributed from one space to the other through unnormalized kernels. We give sufficient conditions for primal attainment and prove a dual formula for this…