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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,…
We recently proposed a new ensemble clustering algorithm for graphs (ECG) based on the concept of consensus clustering. We validated our approach by replicating a study comparing graph clustering algorithms over benchmark graphs, showing…
Bach et al. [1] recently presented an algorithm for constructing confluent drawings, by leveraging power graph decomposition to generate an auxiliary routing graph. We identify two issues with their method which we call the node split and…
The alliance polynomial of a graph $\Gamma$ with order $n$ and maximum degree $\delta_1$ is the polynomial $A(\Gamma; x) = \sum_{k=-\delta_1}^{\delta_1} A_{k}(\Gamma) \, x^{n+k}$, where $A_{k}(\Gamma)$ is the number of exact defensive…
We study strong equilibria in symmetric capacitated cost-sharing games. In these games, a graph with designated source $s$ and sink $t$ is given, and each edge is associated with some cost. Each agent chooses strategically an $s$-$t$ path,…
A graph $G = (V, E)$ is \emph{partitionable} if there exists a partition $\{A, B\}$ of $V$ such that $A$ induces a disjoint union of cliques and $B$ induces a triangle-free graph. In this paper we investigate the computational complexity of…
In this paper we study a resource allocation problem that encodes correlation between items in terms of \conflict and maximizes the minimum utility of the agents under a conflict free allocation. Admittedly, the problem is computationally…
Knowledge graphs (KGs) are an important source repository for a wide range of applications and rule mining from KGs recently attracts wide research interest in the KG-related research community. Many solutions have been proposed for the…
We study a class of nested path problems, in which every path-based variable can be decomposed into a sequence of subpaths. Subpaths must satisfy local resources, while paths must satisfy additional global resources. This paper develops a…
A visualized graph is a powerful tool for data analysis and synthesis tasks. In this case, the task of visualization constitutes not only in displaying vertices and edges according to the graph representation, but also in ensuring that the…
In a graph $G = (V,E)$, a vertex subset $S\subseteq V(G)$ is said to be a dominating set of $G$ if every vertex not in $S$ is adjacent to a vertex in $S$. A dominating set $S$ of $G$ is called a paired-dominating set of $G$ if the induced…
Finding cohesive subgraphs in a network is a well-known problem in graph theory. Several alternative formulations of cohesive subgraph have been proposed, a notable example being $s$-club, which is a subgraph where each vertex is at…
We study the percolation properties of graph partitioning on random regular graphs with N vertices of degree $k$. Optimal graph partitioning is directly related to optimal attack and immunization of complex networks. We find that for any…
In the field of complex networks and graph theory, new results are typically tested on graphs generated by a variety of algorithms such as the Erd\H{o}s-R\'{e}nyi model or the Barab\'{a}si-Albert model. Unfortunately, most graph generating…
An abundance of real-world problems manifest as covering edges and/or vertices of a graph with cliques that are optimized for some objectives. We consider different structural parameters of graph, and design fixed-parameter tractable…
We study a graph partitioning problem motivated by the simulation of the physical movement of multi-body systems on an atomistic level, where the forces are calculated from a quantum mechanical description of the electrons. Several advanced…
Teaming is the process of establishing connections among agents within a system to enable collaboration toward achieving a collective goal. This paper examines teaming in the context of a network of agents learning to coordinate with…
We study the problem of partitioning the edge set of the complete graph into bipartite subgraphs under certain constraints defined by forbidden subgraphs. These constraints lead to both classical problems, such as partitioning into…
Given a $\{0,1\}$-matrix $M$, the graph realization problem for $M$ asks if there exists a spanning forest such that the columns of $M$ are incidence vectors of paths in the forest. The problem is closely related to the recognition of…
We study the problem of instance segmentation in biological images with crowded and compact cells. We formulate this task as an integer program where variables correspond to cells and constraints enforce that cells do not overlap. To solve…