Related papers: Fast Algorithms for the Maximum Clique Problem on …
Extracting cohesive subgraphs from complex networks is a fundamental task in graph analytics and is essential for understanding biological, social, and web graphs. The edge-based $\gamma$-quasi-clique model offers a flexible alternative by…
The Cluster Deletion problem takes a graph $G$ as input and asks for a minimum size set of edges $X$ such that $G-X$ is the disjoint union of complete graphs. An equivalent formulation is the Clique Partition problem, which asks to find a…
A central problem in graph mining is finding dense subgraphs, with several applications in different fields, a notable example being identifying communities. While a lot of effort has been put on the problem of finding a single dense…
We tackle the problem of counting the number of $k$-cliques in large-scale graphs, for any constant $k \ge 3$. Clique counting is essential in a variety of applications, among which social network analysis. Due to its computationally…
Complex networks often exhibit community structure, with communities corresponding to denser subgraphs in which nodes are closely linked. When modelling systems where interactions extend beyond node pairs to arbitrary numbers of nodes,…
Many systems can be described using graphs, or networks. Detecting communities in these networks can provide information about the underlying structure and functioning of the original systems. Yet this detection is a complex task and a…
In the 90's Clark, Colbourn and Johnson wrote a seminal paper where they proved that maximum clique can be solved in polynomial time in unit disk graphs. Since then, the complexity of maximum clique in intersection graphs of d-dimensional…
The NP-hard maximum value preordering problem is both a joint relaxation and a hybrid of the clique partition problem (a clustering problem) and the partial ordering problem. Toward approximate solutions and lower bounds, we introduce a…
Community discovery in the social network is one of the tremendously expanding areas which earn interest among researchers for the past one decade. There are many already existing algorithms. However, new seed-based algorithms establish an…
Many graph mining applications rely on detecting subgraphs which are near-cliques. There exists a dichotomy between the results in the existing work related to this problem: on the one hand the densest subgraph problem (DSP) which maximizes…
Community detection remains an important problem in data mining, owing to the lack of scalable algorithms that exploit all aspects of available data - namely the directionality of flow of information and the dynamics thereof. Most existing…
Numerous graph neural network (GNN)-based algorithms have been proposed to solve graph-based combinatorial optimization problems (COPs), but methods to explain their predictions remain largely undeveloped. We introduce ARM-Explainer, a…
We present a new parallel algorithm for $k$-clique counting/listing that has polylogarithmic span (parallel time) and is work-efficient (matches the work of the best sequential algorithm) for sparse graphs. Our algorithm is based on…
The Edge Interdiction Clique Problem (EICP) aims to remove at most $k$ edges from a graph so as to minimize the size of the largest clique in the remaining graph. This problem captures a fundamental question in graph manipulation: which…
$k$-defective cliques relax cliques by allowing up-to $k$ missing edges from being a complete graph. This relaxation enables us to find larger near-cliques and has applications in link prediction, cluster detection, social network analysis…
Combinatorial optimization problems arise in a wide range of applications from diverse domains. Many of these problems are NP-hard and designing efficient heuristics for them requires considerable time and experimentation. On the other…
A disk graph is an intersection graph of disks in the Euclidean plane, where the disks correspond to the vertices of the graph and a pair of vertices are adjacent if and only if their corresponding disks intersect. The problem of…
In network analysis and graph mining, closeness centrality is a popular measure to infer the importance of a vertex. Computing closeness efficiently for individual vertices received considerable attention. The NP-hard problem of group…
It has been found that many networks display community structure -- groups of vertices within which connections are dense but between which they are sparser -- and highly sensitive computer algorithms have in recent years been developed for…
Finding communities in graphs is one of the most well-studied problems in data mining and social-network analysis. In many real applications, the underlying graph does not have a clear community structure. In those cases, selecting a single…