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Problems of the following kind have been the focus of much recent research in the realm of parameterized complexity: Given an input graph (digraph) on $n$ vertices and a positive integer parameter $k$, find if there exist $k$ edges (arcs)…
We study dynamic planar graphs with $n$ vertices, subject to edge deletion, edge contraction, edge insertion across a face, and the splitting of a vertex in specified corners. We dynamically maintain a combinatorial embedding of such a…
Network interdiction problems by deleting critical nodes have wide applications. However, node deletion is not always feasible in certain practical scenarios. We consider the maximum shortest path interdiction problem by upgrading nodes on…
The network inference problem consists of reconstructing the edge set of a network given traces representing the chronology of infection times as epidemics spread through the network. This problem is a paradigmatic representative of…
The articulation points of an undirected connected graphs are those vertices whose removal increases the number of connected components of the graph, i.e. the vertices whose removal disconnects the graph. However, not all the articulation…
This work addresses the challenge of using a deep learning model to prune graphs and the ability of this method to integrate explainability into spatio-temporal problems through a new approach. Instead of applying explainability to the…
A vertex whose removal in a graph $G$ increases the number of components of $G$ is called a cut vertex. For all $n,c$, we determine the maximum number of connected induced subgraphs in a connected graph with order $n$ and $c$ cut vertices,…
An instance of the Connected Maximum Cut problem consists of an undirected graph G = (V, E) and the goal is to find a subset of vertices S $\subseteq$ V that maximizes the number of edges in the cut \delta(S) such that the induced graph…
In this paper, we continue our development of algorithms used for topological network discovery. We present native P system versions of two fundamental problems in graph theory: finding the maximum number of edge- and node-disjoint paths…
Graphs are fundamental objects that find widespread applications across computer science and beyond. Graph Theory has yielded deep insights about structural properties of various families of graphs, which are leveraged in the design and…
Given a graph $G=(V, E)$, a connected sides cut $(U, V\backslash U)$ or $\delta (U)$ is the set of edges of E linking all vertices of U to all vertices of $V\backslash U$ such that the induced subgraphs $G[U]$ and $G[V\backslash U]$ are…
We consider a natural variant of the well-known Feedback Vertex Set problem, namely the problem of deleting a small subset of vertices or edges to a full binary tree. This version of the problem is motivated by real-world scenarios that are…
We consider two new problems regarding the impact of edge addition or removal on the modularity of partitions (or community structures) in a network. The first problem seeks to add edges to enforce that a desired partition is the partition…
A heavy path in a weighted graph represents a notion of connectivity and ordering that goes beyond two nodes. The heaviest path of length l in the graph, simply means a sequence of nodes with edges between them, such that the sum of edge…
This paper introduces a unified computational framework for the anonymization problem in social networks, where the objective is to maximize node anonymity through graph alterations. We define three variants of the underlying optimization…
We consider edge insertion and deletion operations that increase the connectivity of a given planar straight-line graph (PSLG), while minimizing the total edge length of the output. We show that every connected PSLG $G=(V,E)$ in general…
It is required to find an optimal order of constructing the edges of a network so as to minimize the sum of the weighted connection times of relevant pairs of vertices. Construction can be performed anytime anywhere in the network, with a…
Network structure is a mechanism for promoting cooperation in social dilemma games. In the present study, we explore graph surgery, i.e., to slightly perturb the given network, towards a network that better fosters cooperation. To this end,…
Multilayer networks are a powerful paradigm to model complex systems, where multiple relations occur between the same entities. Despite the keen interest in a variety of tasks, algorithms, and analyses in this type of network, the problem…
As two fundamental problems, graph cuts and graph matching have been investigated over decades, resulting in vast literature in these two topics respectively. However the way of jointly applying and solving graph cuts and matching receives…