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Kernelization studies polynomial-time preprocessing algorithms. Over the last 20 years, the most celebrated positive results of the field have been linear kernels for classical NP-hard graph problems on sparse graph classes. In this paper,…
Combinatorial Optimization (CO) has been a long-standing challenging research topic featured by its NP-hard nature. Traditionally such problems are approximately solved with heuristic algorithms which are usually fast but may sacrifice the…
Vertex covering has important applications for wireless sensor networks such as monitoring link failures, facility location, clustering, and data aggregation. In this study, we designed three algorithms for constructing vertex cover in…
We study the parameterized complexity of transforming graphs into Uniform Cluster graphs, where each component is an equal-sized clique. We consider Uniform Cluster Vertex Deletion (UCVD), Uniform Cluster Edge Deletion (UCED), Uniform…
This paper explores two fundamental concepts: branch width and weak ultrafilter. Branch width is a significant graph width parameter that measures the degree of connectivity in a graph using a branch decomposition and a symmetric submodular…
\textproc{Weighted Vertex Cover} is a variation of an extensively studied NP-complete problem, \textproc{Vertex Cover}, in which we are given a graph, $G = (V,E,w)$, where function $w:V \rightarrow \mathbb{Q}^{+}$ and a parameter $k$. The…
Counting the solution number of combinational optimization problems is an important topic in the study of computational complexity, especially on the #P-complete complexity class. In this paper, we first investigate some organizations of…
Weaknesses in computer systems such as faults, bugs and errors in the architecture, design or implementation of software provide vulnerabilities that can be exploited by attackers to compromise the security of a system. Common Weakness…
As a tool for estimating networks in high dimensions, graphical models are commonly applied to calcium imaging data to estimate functional neuronal connectivity, i.e. relationships between the activities of neurons. However, in many calcium…
Massive network exploration is an important research direction with many applications. In such a setting, the network is, usually, modeled as a graph $G$, whereas any structural information of interest is extracted by inspecting the way…
A popular model to measure network stability is the $k$-core, that is the maximal induced subgraph in which every vertex has degree at least $k$. For example, $k$-cores are commonly used to model the unraveling phenomena in social networks.…
A prototypical graph problem is centered around a graph-theoretic property for a set of vertices and a solution to it is a set of vertices for which the desired property holds. The task is to decide whether, in the given graph, there exists…
In this paper, we study the crucial elements of complex networks, namely nodes, and edges and their properties such as their community structure, which play an important role in dictating the robustness of the network towards structural…
Understanding natural phenomenon through the interactions of different complex systems has become an increasing focus in scientific inquiry. Defining complexity and actually measuring it is an ongoing debate and no standard framework has…
Complex networks are a powerful paradigm to model complex systems. Specific network models, e.g., multilayer networks, temporal networks, and signed networks, enrich the standard network representation with additional information to better…
Betweenness centrality is a fundamental centrality measure in social network analysis. Given a large-scale network, how can we find the most central nodes? This question is of key importance to numerous important applications that rely on…
Motivation: The size of available omics datasets is steadily increasing with technological advancement in recent years. While this increase in sample size can be used to improve the performance of relevant prediction tasks in healthcare,…
Networks are inherently vulnerable to vertex failures, making the analysis of their structural robustness a fundamental problem in graph theory. In this study, we investigate the closeness and vertex residual closeness of graphs, with a…
The CONNECTED VERTEX COVER problem asks for a vertex cover in a graph that induces a connected subgraph. The problem is known to be fixed-parameter tractable (FPT), and is unlikely to have a polynomial sized kernel (under complexity…
Complex functional brain networks are large networks of brain regions and functional brain connections. Statistical characterizations of these networks aim to quantify global and local properties of brain activity with a small number of…