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Given a 2-edge connected, unweighted, and undirected graph $G$ with $n$ vertices and $m$ edges, a $\sigma$-tree spanner is a spanning tree $T$ of $G$ in which the ratio between the distance in $T$ of any pair of vertices and the…
Each vertex of an arbitrary simple graph on $n$ vertices chooses $k$ random incident edges. What is the expected number of edges in the original graph that connect different connected components of the sampled subgraph? We prove that the…
The minimum feedback arc set problem asks to delete a minimum number of arcs (directed edges) from a digraph (directed graph) to make it free of any directed cycles. In this work we approach this fundamental cycle-constrained optimization…
The $k$-center problem is a central optimization problem with numerous applications for machine learning, data mining, and communication networks. Despite extensive study in various scenarios, it surprisingly has not been thoroughly…
Spin glass theory studies the structure of sublevel sets and minima (or near-minima) of certain classes of random functions in high dimension. Near-minima of random functions also play an important role in high-dimensional statistics and…
We study finite-sum nonlinear programs with localized variable coupling encoded by a (hyper)graph. We introduce a graph-compliant decomposition framework that brings message passing into continuous optimization in a rigorous, implementable,…
In this paper we consider a recently developed distributed optimization algorithm based on gradient tracking. We propose a system theory framework to analyze its structural properties on a preliminary, quadratic optimization set-up.…
We study the notion of local treewidth in sparse random graphs: the maximum treewidth over all $k$-vertex subgraphs of an $n$-vertex graph. When $k$ is not too large, we give nearly tight bounds for this local treewidth parameter; we also…
Message-passing algorithms have emerged as powerful techniques for approximate inference in graphical models. When these algorithms converge, they can be shown to find local (or sometimes even global) optima of variational formulations to…
We focus on the commonly used synchronous Gradient Descent paradigm for large-scale distributed learning, for which there has been a growing interest to develop efficient and robust gradient aggregation strategies that overcome two key…
We revisit the classical hard-core model, also known as independent set and dual to vertex cover problem, where one puts particles with a first-neighbor hard-core repulsion on the vertices of a random graph. Although the case of random…
A $k$-decision tree $t$ (or $k$-tree) is a recursive partition of a matrix (2D-signal) into $k\geq 1$ block matrices (axis-parallel rectangles, leaves) where each rectangle is assigned a real label. Its regression or classification loss to…
Computing $(k,\eta)$-cores from uncertain graphs is a fundamental problem in uncertain graph analysis. UCF-Index is the state-of-the-art resolution to support $(k,\eta)$-core queries, allowing the $(k,\eta)$-core for any combination of $k$…
We show how to construct an overlay network of constant degree and diameter $O(\log n)$ in time $O(\log n)$ starting from an arbitrary weakly connected graph. We assume a synchronous communication network in which nodes can send messages to…
A tree $\sigma$-spanner of a positively real-weighted $n$-vertex and $m$-edge undirected graph $G$ is a spanning tree $T$ of $G$ which approximately preserves (i.e., up to a multiplicative stretch factor $\sigma$) distances in $G$. Tree…
We propose Graph Tree Networks (GTNets), a deep graph learning architecture with a new general message passing scheme that originates from the tree representation of graphs. In the tree representation, messages propagate upward from the…
The information rate for an access structure is the reciprocal of the load of the optimal secret sharing scheme for this structure. We determine this value for all trees: it is 1/(2-1/c), where c is the size of the largest core of the tree.…
Quantum algorithms provide a promising framework in high-energy physics, in particular, for unraveling the causal configurations of multiloop Feynman diagrams by identifying Feynman propagators with qubits, a challenge analogous to querying…
We consider the strongly NP-hard single-machine coupled task scheduling problem with exact delays to minimize the makespan. In this problem, a set of jobs has to be scheduled, each composed of two tasks interspersed by an exact delay. Given…
Hypergraphs are higher-order networks that capture the interactions between two or more nodes. Hypergraphs can always be represented by factor graphs, i.e. bipartite networks between nodes and factor nodes (representing groups of nodes).…