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The pseudoinverse of a graph Laplacian is used in many applications and fields, such as for instance in the computation of the effective resistance in electrical networks, in the calculation of the hitting/commuting times for a Markov chain…
In this article, we present the first deterministic directed Laplacian L systems solver that runs in time almost-linear in the number of non-zero entries of L. Previous reductions imply the first deterministic almost-linear time algorithms…
We present a derivative-based algorithm for nonlinearly constrained optimization problems that is tolerant of inaccuracies in the data. The algorithm solves a semi-smooth set of nonlinear equations that are equivalent to the first-order…
Policy gradient methods are among the most effective methods in challenging reinforcement learning problems with large state and/or action spaces. However, little is known about even their most basic theoretical convergence properties,…
Many discrete optimization problems amount to selecting a feasible set of edges of least weight. We consider in this paper the context of spatial graphs where the positions of the vertices are uncertain and belong to known uncertainty sets.…
Given an undirected graph, one can assign directions to each of the edges of the graph, thus orienting the graph. To be as egalitarian as possible, one may wish to find an orientation such that no vertex is unfairly hit with too many arcs…
Given a pair of graphs with the same number of vertices, the inexact graph matching problem consists in finding a correspondence between the vertices of these graphs that minimizes the total number of induced edge disagreements. We study…
Consider the twin problems of estimating the connection probability matrix of an inhomogeneous random graph and the graphon of a W-random graph. We establish the minimax estimation rates with respect to the cut metric for classes of block…
An optimum solution free from degeneration is found to the system of linear algebraic equations with empirical coefficients and right-hand sides. The quadratic risk of estimators of the unknown solution vector is minimized over a class of…
We propose a structure-preserving model-reduction methodology for large-scale dynamic networks with tightly-connected components. First, the coherent groups are identified by a spectral clustering algorithm on the graph Laplacian matrix…
This paper shows that graph spectral embedding using the random walk Laplacian produces vector representations which are completely corrected for node degree. Under a generalised random dot product graph, the embedding provides uniformly…
Relaxation processes driven by a Laplacian matrix can be found in many real-world big-data systems, for example, in search engines on the World-Wide-Web and the dynamic load balancing protocols in mesh networks. To numerically implement…
Graphs are commonly used to model various complex systems, including social networks, power grids, transportation networks, and biological systems. In many applications, the connectivity of these networks can be expressed through the Mean…
This paper applies techniques from algebraic and differential geometry to determine how to best pack points in real projective spaces. We present a computer-assisted proof of the optimality of a particular 6-packing in…
We consider the problem of exact and inexact matching of weighted undirected graphs, in which a bijective correspondence is sought to minimize a quadratic weight disagreement. This computationally challenging problem is often relaxed as a…
We consider a decision network on an undirected graph in which each node corresponds to a decision variable, and each node and edge of the graph is associated with a reward function whose value depends only on the variables of the…
The "exact subgraph" approach was recently introduced as a hierarchical scheme to get increasingly tight semidefinite programming relaxations of several NP-hard graph optimization problems. Solving these relaxations is a computational…
The graph Laplacian, a typical representation of a network, is an important matrix that can tell us much about the network structure. In particular its eigenpairs (eigenvalues and eigenvectors) incubate precious topological information…
Computing high-quality graph partitions is a challenging problem with numerous applications. In this paper, we present a novel meta-heuristic for the balanced graph partitioning problem. Our approach is based on integer linear programs that…
Considering the paradigmatic driven Brownian motion, we perform extensive numerical analysis on the performance of optimal linear-response processes far from equilibrium. We focus on the overdamped regime where exact optimal processes are…