Related papers: On the expected moments between two identical rand…

We study optimal transport for stationary stochastic processes taking values in finite spaces. In order to reflect the stationarity of the underlying processes, we restrict attention to stationary couplings, also known as joinings. The…

For a fixed integer $k\geqslant 2$, let $G\in \mathcal{G}(n,p)$ be a simple connected graph on $n\rightarrow\infty$ vertices with the expected degree $d=np$ satisfying $d\geqslant c$ and $d^{k-1}= o(n)$ for some large enough constant $c$.…

Consider $n$ mobile sensors placed independently at random with the uniform distribution on a barrier represented as the unit line segment $[0,1]$. The sensors have identical sensing radius, say $r$. When a sensor is displaced on the line a…

The biharmonic distance is a fundamental metric on graphs that measures the dissimilarity between two nodes, capturing both local and global structures. It has found applications across various fields, including network centrality, graph…

We propose a simple subsampling scheme for fast randomized approximate computation of optimal transport distances. This scheme operates on a random subset of the full data and can use any exact algorithm as a black-box back-end, including…

We consider random i.i.d. samples of absolutely continuous measures on bounded connected domains. We prove an upper bound on the $\infty$-transportation distance between the measure and the empirical measure of the sample. The bound is…

We investigate the optimal design of networks for a general transport system. Our network is built from a regular two-dimensional ($d=2$) square lattice to be improved by adding long-range connections (shortcuts) with probability $P_{ij}…

We propose a new framework for formulating optimal transport distances between Markov chains. Previously known formulations studied couplings between the entire joint distribution induced by the chains, and derived solutions via a reduction…

In graph analysis, a classic task consists in computing similarity measures between (groups of) nodes. In latent space random graphs, nodes are associated to unknown latent variables. One may then seek to compute distances directly in the…

We study the NP-hard problem of approximating a Minimum Routing Cost Spanning Tree in the message passing model with limited bandwidth (CONGEST model). In this problem one tries to find a spanning tree of a graph $G$ over $n$ nodes that…

In this paper we analyze the expected time complexity of the auction algorithm for the matching problem on random bipartite graphs. We prove that the expected time complexity of the auction algorithm for bipartite matching is…

We consider robust variants of the standard optimal transport, named robust optimal transport, where marginal constraints are relaxed via Kullback-Leibler divergence. We show that Sinkhorn-based algorithms can approximate the optimal cost…

We study Benamou's domain decomposition algorithm for optimal transport in the entropy regularized setting. The key observation is that the regularized variant converges to the globally optimal solution under very mild assumptions. We prove…

We give a statistical interpretation of entropic optimal transport by showing that performing maximum-likelihood estimation for Gaussian deconvolution corresponds to calculating a projection with respect to the entropic optimal transport…

Finding an optimal assignment between two sets of objects is a fundamental problem arising in many applications, including the matching of `bag-of-words' representations in natural language processing and computer vision. Solving the…

Optimal mass transport is described by an approximation of transport cost via semi-discrete costs. The notions of optimal partition and optimal strong partition are given as well. We also suggest an algorithm for computation of Optimal…

In this work, we propose a novel machine learning approach to compute the optimal transport map between two continuous distributions from their unpaired samples, based on the DeepParticle methods. The proposed method leads to a min-min…

We study the on-line minimum weighted bipartite matching problem in arbitrary metric spaces. Here, $n$ not necessary disjoint points of a metric space $M$ are given, and are to be matched on-line with $n$ points of $M$ revealed one by one.…

In the infinite regular tree $\mathbb{T}_{q+1}$ with $q \in \mathbb{Z}_{\ge 2}$, we consider families $\{\mu_u^n\}$, indexed by vertices $u$ and nonnegative integers ("discrete time steps") $n$, of probability measures such that $\mu_u^n(v)…

In Delay Tolerant Networks (DTNs), two-hop routing compromises energy versus delay more conveniently than epidemic routing. Literature provides comprehensive results on optimal routing policies for mobile nodes with homogeneous mobility,…