Related papers: Determining r- and (r,s)-Robustness of Digraphs Us…
Computing the number of realizations of a minimally rigid graph is a notoriously difficult problem. Towards this goal, for graphs that are minimally rigid in the plane, we take advantage of a recently published algorithm, which is the…
Graphs are a natural representation for systems based on relations between connected entities. Combinatorial optimization problems, which arise when considering an objective function related to a process of interest on discrete structures,…
One major obstacle that precludes the success of reinforcement learning in real-world applications is the lack of robustness, either to model uncertainties or external disturbances, of the trained policies. Robustness is critical when the…
Many approaches for verifying input-output properties of neural networks have been proposed recently. However, existing algorithms do not scale well to large networks. Recent work in the field of model compression studied binarized neural…
Consider a graph $G=(V,E)$ without isolated edges and with maximum degree $\Delta$. Given a colouring $c:E\to\{1,2,\ldots,k\}$, the weighted degree of a vertex $v\in V$ is the sum of its incident colours, i.e., $\sum_{e\ni v}c(e)$. For any…
Large scale graph optimization problems arise in many fields. This paper presents an extensible, high performance framework (named OpenGraphGym-MG) that uses deep reinforcement learning and graph embedding to solve large graph optimization…
Delsarte, Goethals, and Seidel (1977) used the linear programming method in order to find bounds for the size of spherical codes endowed with prescribed inner products between distinct points in the code. In this paper, we develop the…
This paper investigates a combinatorial optimization problem motived from a secure power network design application in [D\'{a}n and Sandberg 2010]. Two equivalent graph optimization formulations are derived. One of the formulations is a…
This thesis develops data-driven machine learning algorithms to managing and optimizing the next-generation highly complex cyberphysical systems, which desperately need ground-breaking control, monitoring, and decision making schemes that…
Although deep learning (DL) has received much attention in accelerated magnetic resonance imaging (MRI), recent studies show that tiny input perturbations may lead to instabilities of DL-based MRI reconstruction models. However, the…
Many computational problems admit fast algorithms on special inputs, however, the required properties might be quite restrictive. E.g., many graph problems can be solved much faster on interval or cographs, or on graphs of small…
We address the problem of merging graph and feature-space information while learning a metric from structured data. Existing algorithms tackle the problem in an asymmetric way, by either extracting vectorized summaries of the graph…
Graph is a fundamental mathematical structure in characterizing relations between different objects and has been widely used on various learning tasks. Most methods implicitly assume a given graph to be accurate and complete. However, real…
Understanding how the optimal value of an optimisation problem changes when its input data is modified is an old question in mathematical optimisation. This paper investigates the computation of the optimal values of a family of (possibly…
An important measure of signed graphs is the line index of balance which has several applications in many fields. However, this graph-theoretic measure was underused for decades because of the inherent complexity in its computation which is…
Scaled relative graphs (SRGs) enable graphical analysis and design of nonlinear systems. In this paper, we present a systematic approach for computing both soft and hard SRGs of nonlinear systems using dynamic integral quadratic constraints…
This paper addresses a resilient exponential distributed convex optimization problem for a heterogeneous linear multi-agent system under Denial-of-Service (DoS) attacks over random digraphs. The random digraphs are caused by unreliable…
Graph-regularized semi-supervised learning has been used effectively for classification when (i) instances are connected through a graph, and (ii) labeled data is scarce. If available, using multiple relations (or graphs) between the…
In this paper, we propose a graph classification approach for automatically determining whether to use a monolithic or a decomposition-based solution method. In this approach, an optimization problem is represented as a graph that captures…
Neural networks have become increasingly popular in controller design due to their versatility and efficiency. However, their integration into feedback systems can pose stability challenges, particularly in the presence of uncertainties.…