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Finding important nodes in a graph and measuring their importance is a fundamental problem in the analysis of social networks, transportation networks, biological systems, etc. Among popular such metrics are graph centrality, betweenness…

Feature selection is an important and active research area in statistics and machine learning. The Elastic Net is often used to perform selection when the features present non-negligible collinearity or practitioners wish to incorporate…

An NP-hard problem is considered of intersecting a given set of $n$ straight line segments on the plane with the smallest cardinality set of disks of fixed radii $r>0,$ where the set of segments forms a straight line drawing $G=(V,E)$ of a…

This paper studies the Craig variant of the Golub-Kahan bidiagonalization algorithm as an iterative solver for linear systems with saddle point structure. Such symmetric indefinite systems in 2x2 block form arise in many applications, but…

Convergence guarantees of many resilient consensus algorithms are based on the graph theoretic properties of $r$- and $(r,s)$-robustness. These algorithms guarantee consensus of normally behaving agents in the presence of a bounded number…

In this work, we propose an optimization framework for estimating a sparse robust one-dimensional subspace. Our objective is to minimize both the representation error and the penalty, in terms of the l1-norm criterion. Given that the…

Finding patterns in graphs is a fundamental problem in databases and data mining. In many applications, graphs are temporal and evolve over time, so we are interested in finding durable patterns, such as triangles and paths, which persist…

A crucial challenge in engineering modern, integrated systems is to produce robust designs. Ensuring robust design is difficult because subsystem couplings produce unpredictable response to changes in whole system specifications. Here, we…

There has been an increase in the use of resilient control algorithms based on the graph theoretic properties of $r$- and $(r,s)$-robustness. These algorithms guarantee consensus of normally behaving agents in the presence of a bounded…

The graph matching problem is a significant special case of the Quadratic Assignment Problem, with extensive applications in pattern recognition, computer vision, protein alignments and related fields. As the problem is NP-hard, relaxation…

Given positive integers $a_1,..., a_n, t$, the fixed weight subset sum problem is to find a subset of the $a_i$ that sum to $t$, where the subset has a prescribed number of elements. It is this problem that underlies the security of modern…

Grouping the nodes of a graph into clusters is a standard technique for studying networks. We study a problem where we are given a directed network and are asked to partition the graph into a sequence of coherent groups. We assume that…

Recovering the digital input of a time-discrete linear system from its (noisy) output is a significant challenge in the fields of data transmission, deconvolution, channel equalization, and inverse modeling. A variety of algorithms have…

Speed-robust scheduling is the following two-stage problem of scheduling $n$ jobs on $m$ uniformly related machines. In the first stage, the algorithm receives the value of $m$ and the processing times of $n$ jobs; it has to partition the…

This work establishes a solution to the problem of assessing the capacity of multi-object assemblies to withstand external forces without becoming unstable. Our physically-grounded approach handles arbitrary structures made from rigid…

Robustness estimation is critical for the design and maintenance of resilient networks, one of the global challenges of the 21st century. Existing studies exploit network metrics to generate attack strategies, which simulate intentional…

Graph rigidity theory studies the capability of a graph embedded in the Euclidean space to constrain its global geometric shape via local constraints among nodes and edges, and has been widely exploited in network localization and formation…

While operating communication networks adaptively may improve utilization and performance, frequent adjustments also introduce an algorithmic challenge: the re-optimization of traffic engineering solutions is time-consuming and may limit…

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.…

The Carleman embedding method is a widely used technique for linearizing a system of nonlinear differential equations, but fails to converge in regions where there are multiple fixed points. We propose and test three different versions of a…