Related papers: Using modular decomposition technique to solve the…
For clustering of an undirected graph, this paper presents an exact algorithm for the maximization of modularity density, a more complicated criterion to overcome drawbacks of the well-known modularity. The problem can be interpreted as the…
Finding "densely connected clusters" in a graph is in general an important and well studied problem in the literature \cite{Schaeffer}. It has various applications in pattern recognition, social networking and data mining…
A hedge graph is a graph whose edge set has been partitioned into groups called hedges. Here we consider a generalization of the well-known \textsc{Cluster Deletion} problem, named \textsc{Hedge Cluster Deletion}. The task is to compute the…
We introduce a new method for decomposing the edge set of a graph, and use it to replace the Regularity lemma of Szemer\'edi in some graph embedding problems. An algorithmic version is also given.
Although it has been claimed in two different papers that the maximum cardinality cut problem is polynomial-time solvable for proper interval graphs, both of them turned out to be erroneous. In this paper, we give FPT algorithms for the…
Graph clustering is a fundamental and challenging task in the field of graph mining where the objective is to group the nodes into clusters taking into consideration the topology of the graph. It has several applications in diverse domains…
How to obtain a graph from data samples is an important problem in graph signal processing. One way to formulate this graph learning problem is based on Gaussian maximum likelihood estimation, possibly under particular topology constraints.…
This paper assesses the performance of the D-Wave 2X (DW) quantum annealer for finding a maximum clique in a graph, one of the most fundamental and important NP-hard problems. Because the size of the largest graphs DW can directly solve is…
We consider the problem of identifying the densest k-node subgraph in a given graph. We write this problem as an instance of rank-constrained cardinality minimization and then relax using the nuclear and 11 norms. Although the original…
In this article we present the idea of clique ceiling numbers of the vertices of a given graph that has a universal vertex. We follow up with a polynomial-time algorithm to compute an upper bound for the clique number of such a graph using…
A vertex set $X$ of a graph $G$ is an association set if each component of $G - X$ is a clique, or a dissociation set if each component of $G - X$ is a single vertex or a single edge. Interestingly, $G - X$ is then precisely a graph…
This paper deals with the problem of finding, for a given graph and a given natural number k, a subgraph of k nodes with a maximum number of edges. This problem is known as the k-cluster problem and it is NP-hard on general graphs as well…
This work examines the problem of clique enumeration on a graph by exploiting its clique covers. The principle of inclusion/exclusion is applied to determine the number of cliques of size $r$ in the graph union of a set $\mathcal{C} =…
Spanning tree modulus is a generalization of effective resistance that is closely related to graph strength and fractional arboricity. The optimal edge density associated with spanning tree modulus is known to produce two hierarchical…
In this paper, we develop a new decomposition technique for solving bi-objective linear programming problems. The proposed methodology combines the bi-objective simplex algorithm with Benders decomposition and can be used to obtain a…
Cliques, groups of fully connected nodes in a network, are often used to study group dynamics of complex systems. In real-world settings, group dynamics often have a temporal component. For example, conference attendees moving from one…
Benders decomposition is a widely used method for solving large optimization problems, but its performance is often hindered by the repeated solution of subproblems. We propose a flexible and modular algorithmic framework for accelerating…
We are interested in multilayer graph clustering, which aims at dividing the graph nodes into categories or communities. To do so, we propose to learn a clustering-friendly embedding of the graph nodes by solving an optimization problem…
A connected matching in a graph G consists of a set of pairwise disjoint edges whose covered vertices induce a connected subgraph of G. While finding a connected matching of maximum cardinality is a well-solved problem, it is NP-hard to…
Cluster detection plays a fundamental role in the analysis of data. In this paper, we focus on the use of s-defective clique models for network-based cluster detection and propose a nonlinear optimization approach that efficiently handles…