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Given a vertex-weighted graph, the maximum weight independent set problem asks for a pair-wise non-adjacent set of vertices such that the sum of their weights is maximum. The branch-and-reduce paradigm is the de facto standard approach to…

Security assessment is one of the most crucial functions of a power system operator. However, growing complexity and unpredictability make this an increasingly complex and computationally difficult task. In recent times, machine learning…

An independent transversal (IT) in a graph with a given vertex partition is an independent set consisting of one vertex in each partition class. Several sufficient conditions are known for the existence of an IT in a given graph with a…

The factor graph of an instance of a symmetric constraint satisfaction problem on n Boolean variables and m constraints (CSPs such as k-SAT, k-AND, k-LIN) is a bipartite graph describing which variables appear in which constraints. The…

We tackle three optimization problems in which a colored graph, where each node is assigned a color, must be partitioned into colorful connected components. A component is defined as colorful if each color appears at most once. The problems…

CySecTool is a tool that finds a cost-optimal security controls portfolio in a given budget for a probabilistic attack graph. A portfolio is a set of counter-measures, or controls, against vulnerabilities adopted for a computer system,…

Graph matching is a fundamental problem in pattern recognition, with many applications such as software analysis and computational biology. One well-known type of graph matching problem is graph isomorphism, which consists of deciding if…

We provide a graphical treatment of SAT and #SAT on equal footing. Instances of #SAT can be represented as tensor networks in a standard way. These tensor networks are interpreted by diagrams of the ZH-calculus: a system to reason about…

Combinatorial optimization is essential across numerous disciplines. Traditional metaheuristics excel at exploring complex solution spaces efficiently, yet they often struggle with scalability. Deep learning has become a viable alternative…

Selecting the optimal set of countermeasures is a challenging task that involves various considerations and tradeoffs such as prioritizing the risks to mitigate and costs. The vast majority of studies for selecting a countermeasure…

We consider the incomplete multi-graph matching problem, which is a generalization of the NP-hard quadratic assignment problem for matching multiple finite sets. Multi-graph matching plays a central role in computer vision, e.g., for…

Well-graded families, extremal systems and maximum systems (the last two in the sense of VC-theory and Sauer-Shelah lemma on VC-dimension) are three important classes of set systems. This paper aims to study the notion of duality in the…

Node classification and graph classification are two graph learning problems that predict the class label of a node and the class label of a graph respectively. A node of a graph usually represents a real-world entity, e.g., a user in a…

In this paper we give a method to associate a graph with an arbitrary density matrix referred to a standard orthonormal basis in the Hilbert space of a finite dimensional quantum system. We study the related issues like classification of…

Investigation of the market graph attracts a growing attention in market network analysis. One of the important problem connected with market graph is to identify it from observations. Traditional way for the market graph identification is…

We show a method resulting in the improvement of several polynomial-space, exponential-time algorithms. An instance of the problem Max (r,2)-CSP, or simply Max 2-CSP, is parametrized by the domain size r (often 2), the number of variables n…

Assume that a graph $G$ models a detection system for a facility with a possible "intruder," or a multiprocessor network with a possible malfunctioning processor. We consider the problem of placing (the minimum number of) detectors at a…

In this paper, we aim to develop a method for automatically detecting and tracking topics in broadcast news. We present a hierarchical And-Or graph (AOG) to jointly represent the latent structure of both texts and visuals. The AOG embeds a…

Building automation systems (BAS) are interlinked networks of hardware and software, which monitor and control events in the buildings. One of the data communication protocols used in BAS is Building Automation and Control networking…

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…