Related papers: Relative Entropy-Regularized Optimal Transport on …
This article introduces a new class of fast algorithms to approximate variational problems involving unbalanced optimal transport. While classical optimal transport considers only normalized probability distributions, it is important for…
Graph neural networks (GNNs) have shown advantages in graph-based analysis tasks. However, most existing methods have the homogeneity assumption and show poor performance on heterophilic graphs, where the linked nodes have dissimilar…
We propose a novel exact algorithm for the transportation problem, one of the paradigmatic network optimization problems. The algorithm, denoted Iterated Inside Out, requires in input a basic feasible solution and is composed by two main…
In this paper, we consider the problem of scheduling real-time traffic in wireless networks under a conflict-graph interference model and single-hop traffic. The objective is to guarantee that at least a certain fraction of packets of each…
Despite technological advancements, the significance of interdisciplinary subjects like complex networks has grown. Exploring communication within these networks is crucial, with traffic becoming a key concern due to the expanding…
We provide universally-optimal distributed graph algorithms for $(1+\varepsilon)$-approximate shortest path problems including shortest-path-tree and transshipment. The universal optimality of our algorithms guarantees that, on any $n$-node…
This note aims to demonstrate that performing maximum-likelihood estimation for a mixture model is equivalent to minimizing over the parameters an optimal transport problem with entropic regularization. The objective is pedagogical: we seek…
This paper presents the results of an experimental study of graph partitioning. We describe a new heuristic technique, path optimization, and its application to two variations of graph partitioning: the max_cut problem and the…
This work elaborates on the important problem of (1) designing optimal randomized routing policies for reaching a target node t from a source note s on a weighted directed graph G and (2) defining distance measures between nodes…
We analyze optimal transport problems with additional entropic cost evaluated along curves in the Wasserstein space which join two probability measures $m_0,m_1$. The effect of the additional entropy functional results into an elliptic…
We investigate algorithms to find short paths in spatial networks with stochastic edge weights. Our formulation of the problem of finding short paths differs from traditional formulations because we specifically do not make two of the usual…
The goal of regression and classification methods in supervised learning is to minimize the empirical risk, that is, the expectation of some loss function quantifying the prediction error under the empirical distribution. When facing scarce…
We present a comparative study of the application of a recently introduced heuristic algorithm to the optimization of transport on three major types of complex networks. The algorithm balances network traffic iteratively by minimizing the…
This paper considers the vehicle routing problem with stochastic demands (VRPSD) under optimal restocking. We develop an exact algorithm that is effective for solving instances with many vehicles and few customers per route. In our…
In this paper, we consider the problem of recovering the $W_2$-optimal transport map T between absolutely continuous measures $\mu,\nu\in\mathcal{P}(\mathbb{R}^n)$ as the flow of a linear-control neural ODE, where the control depends only…
We consider the optimal control problem of steering an agent population to a desired distribution over an infinite horizon. This is an optimal transport problem over dynamical systems, which is challenging due to its high computational…
Adding entropic regularization to Optimal Transport (OT) problems has become a standard approach for designing efficient and scalable solvers. However, regularization introduces a bias from the true solution. To mitigate this bias while…
We revisit the classic problem of dynamically maintaining shortest paths between all pairs of nodes of a directed weighted graph. The allowed updates are insertions and deletions of nodes and their incident edges. We give worst-case…
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…
In this invited contribution, we revisit the stochastic shortest path problem, and show how recent results allow one to improve over the classical solutions: we present algorithms to synthesize strategies with multiple guarantees on the…