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Preferential attachment is an appealing edge generating mechanism for modeling social networks. It provides both an intuitive description of network growth and an explanation for the observed power laws in degree distributions. However,…
This paper introduces the Simultaneous assignment problem. Let us given a graph with a weight and a capacity function on its edges, and a set of its subgraphs along with a degree upper bound function for each of them. We are also given a…
We study the averaging-based distributed optimization solvers over random networks. We show a general result on the convergence of such schemes using weight-matrices that are row-stochastic almost surely and column-stochastic in expectation…
Graph neural networks (GNNs) have found application for learning in the space of algorithms. However, the algorithms chosen by existing research (sorting, Breadth-First search, shortest path finding, etc.) usually align perfectly with a…
This paper studies the problem of matching two complete graphs with edge weights correlated through latent geometries, extending a recent line of research on random graph matching with independent edge weights to geometric models.…
We consider interacting urns on a finite directed network, where both sampling and reinforcement processes depend on the nodes of the network. This extends previous research by incorporating node-dependent sampling and reinforcement. We…
Graph neural networks compute node representations by performing multiple message-passing steps that consist in local aggregations of node features. Having deep models that can leverage longer-range interactions between nodes is hindered by…
Consider a collection of random variables attached to the vertices of a graph. The reconstruction problem requires to estimate one of them given `far away' observations. Several theoretical results (and simple algorithms) are available when…
This paper deals with the problem of graph matching or network alignment for Erd\H{o}s--R\'enyi graphs, which can be viewed as a noisy average-case version of the graph isomorphism problem. Let $G$ and $G'$ be $G(n, p)$ Erd\H{o}s--R\'enyi…
We study the problem of recovering a planted matching in randomly weighted complete bipartite graphs $K_{n,n}$. For some unknown perfect matching $M^*$, the weight of an edge is drawn from one distribution $P$ if $e \in M^*$ and another…
The stable matching problem is a prototype model in economics and social sciences where agents act selfishly to optimize their own satisfaction, subject to mutually conflicting constraints. A stable matching is a pairing of adjacent…
We study the so-called distributed two-time-scale gradient method for solving convex optimization problems over a network of agents when the communication bandwidth between the nodes is limited, and so information that is exchanged between…
Perfect Matching-Cut is the problem of deciding whether a graph has a perfect matching that contains an edge-cut. We show that this problem is NP-complete for planar graphs with maximum degree four, for planar graphs with girth five, for…
Time series forecasting is often fundamental to scientific and engineering problems and enables decision making. With ever increasing data set sizes, a trivial solution to scale up predictions is to assume independence between interacting…
By collecting and expanding several numerical recipes developed in previous work, we implement an object-oriented Python code, based on the networkX library, for the realization of the configuration model and Newman rewiring. The software…
We consider a matching problem in a bipartite graph $G$ where every vertex has a capacity and a strict preference order on its neighbors. Furthermore, there is a cost function on the edge set. We assume $G$ admits a perfect matching, i.e.,…
For a wireless multi-tier heterogeneous network with orthogonal spectrum allocation across tiers, we optimize the association probability and the fraction of spectrum allocated to each tier so as to maximize rate coverage. In practice, the…
We introduce a model for a growing random graph based on simultaneous reproduction of the vertices. The model can be thought of as a generalisation of the reproducing graphs of Southwell and Cannings and Bonato et al to allow for a random…
Existence of a perfect matching in a random bipartite digraph with bipartition $(V_1, V_2)$, $|V_i|=n$, is studied. The graph is generated in two rounds of random selections of a potential matching partner such that the average number of…
We introduce a `concrete complexity' model for studying algorithms for matching in bipartite graphs. The model is based on the "demand query" model used for combinatorial auctions. Most (but not all) known algorithms for bipartite matching…