Related papers: Multiplicity and Diversity: Analyzing the Optimal …
This work considers clustering nodes of a largely incomplete graph. Under the problem setting, only a small amount of queries about the edges can be made, but the entire graph is not observable. This problem finds applications in…
In the Coloured Clustering problem, we wish to colour vertices of an edge coloured graph to produce as many stable edges as possible, i.e., edges with the same colour as their ends. In this paper, we reveal that the problem is in fact a…
Relationship between agents can be conveniently represented by graphs. When these relationships have different modalities, they are better modelled by multilayer graphs where each layer is associated with one modality. Such graphs arise…
Grouping the nodes of a graph into clusters is a standard technique for studying networks. We study a problem where we are given a directed network and are asked to partition the graph into a sequence of coherent groups. We assume that…
We continue the investigation of problems concerning correlation clustering or clustering with qualitative information, which is a clustering formulation that has been studied recently. The basic setup here is that we are given as input a…
Spectral clustering methods which are frequently used in clustering and community detection applications are sensitive to the specific graph constructions particularly when imbalanced clusters are present. We show that ratio cut (RCut) or…
The most commonly used method to tackle the graph partitioning problem in practice is the multilevel approach. During a coarsening phase, a multilevel graph partitioning algorithm reduces the graph size by iteratively contracting nodes and…
We consider a variant of the clustering problem for a complete weighted graph. The aim is to partition the nodes into clusters maximizing the sum of the edge weights within the clusters. This problem is known as the clique partitioning…
We study the imbalance problem on complete bipartite graphs. The imbalance problem is a graph layout problem and is known to be NP-complete. Graph layout problems find their applications in the optimization of networks for parallel computer…
Correlation Clustering is a powerful graph partitioning model that aims to cluster items based on the notion of similarity between items. An instance of the Correlation Clustering problem consists of a graph $G$ (not necessarily complete)…
Graph clustering is a fundamental computational problem with a number of applications in algorithm design, machine learning, data mining, and analysis of social networks. Over the past decades, researchers have proposed a number of…
The Maximum Balanced Subgraph Problem (MBSP) is the problem of finding a subgraph of a signed graph that is balanced and maximizes the cardinality of its vertex set. We are interested in the exact solution of the problem: an improved…
Given a simple connected graph $G = (V, E)$, we seek to partition the vertex set $V$ into $k$ non-empty parts such that the subgraph induced by each part is connected, and the partition is maximally balanced in the way that the maximum…
Spectral clustering is popular among practitioners and theoreticians alike. While performance guarantees for spectral clustering are well understood, recent studies have focused on enforcing ``fairness'' in clusters, requiring them to be…
Matchings and coverings are central topics in graph theory. The close relationship between these two has been key to many fundamental algorithmic and polyhedral results. For mixed graphs, the notion of matching forest was proposed as a…
Graph based clustering is one of the major clustering methods. Most of it work in three separate steps: similarity graph construction, clustering label relaxing and label discretization with k-means. Such common practice has three…
Optimal geometrical arrangements, such as the stacking of atoms, are of relevance in diverse disciplines. A classic problem is the determination of the optimal arrangement of spheres in three dimensions in order to achieve the highest…
Multilayer graphs are appealing mathematical tools for modeling multiple types of relationship in the data. In this paper, we aim at analyzing multilayer graphs by properly combining the information provided by individual layers, while…
Signed networks, characterized by edges labeled as either positive or negative, offer nuanced insights into interaction dynamics beyond the capabilities of unsigned graphs. Central to this is the task of identifying the maximum balanced…
The benefits of a recently proposed method to approximate hard optimization problems are demonstrated on the graph partitioning problem. The performance of this new method, called Extremal Optimization, is compared to Simulated Annealing in…