Related papers: Fast Algorithms for the Maximum Clique Problem on …
Link streams model interactions over time, and a clique in a link stream is defined as a set of nodes and a time interval such that all pairs of nodes in this set interact permanently during this time interval. This notion was introduced…
A multigraph $G = (V, E)$ is $(k, \ell)$-sparse if every subset $X \subseteq V$ induces at most $\max\{k|X| - \ell, 0\}$ edges. Finding a maximum-size $(k, \ell)$-sparse subgraph is a classical problem in rigidity theory and combinatorial…
The diameter of a graph is among its most basic parameters. Since a few years, it moreover became a key issue to compute it for massive graphs in the context of complex network analysis. However, known algorithms, including the ones…
The higher-order correlation clustering problem for a graph $G$ and costs associated with cliques of $G$ consists in finding a clustering of $G$ so as to minimize the sum of the costs of those cliques whose nodes all belong to the same…
Clique-width is a well-studied graph parameter. For graphs of bounded clique-width, many problems that are NP-hard in general can be polynomial-time solvable. The fact motivates several studies to investigate whether the clique-width of…
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 graph modification problems, one is given a graph G and the goal is to apply a minimum number of modification operations (such as edge deletions) to G such that the resulting graph fulfills a certain property. For example, the Cluster…
All the work made so far on edge-covering a graph by cliques focus on finding the minimum number of cliques that cover the graph. On this paper, we fix the number of cliques that cover a graph by the same number of vertices that the graph…
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…
Parameterized complexity theory has enabled a refined classification of the difficulty of NP-hard optimization problems on graphs with respect to key structural properties, and so to a better understanding of their true difficulties. More…
We consider the enumeration of maximal bipartite cliques (bicliques) from a large graph, a task central to many practical data mining problems in social network analysis and bioinformatics. We present novel parallel algorithms for the…
A dominating set D in a graph G is a subset of its vertices such that every vertex of the graph which does not belong to set D is adjacent to at least one vertex from set D. A set of vertices of graph G is a global dominating set if it is a…
A graph is $k$-degenerate if any induced subgraph has a vertex of degree at most $k$. In this paper we prove new algorithms for cliques and similar structures for these graphs. We design linear time Fixed-Parameter Tractable algorithms for…
We present faster algorithms for approximate maximum flow in undirected graphs with good separator structures, such as bounded genus, minor free, and geometric graphs. Given such a graph with $n$ vertices, $m$ edges along with a recursive…
The monography presents a new algorithm for finding the clique of maximal length in a nonseparable graph. The algorithm is based on the properties of the representation of a clique as a subset of the set of cycles with a length of three,…
Graph clustering is an important algorithmic technique for analysing massive graphs, and has been widely applied in many research fields of data science. While the objective of most graph clustering algorithms is to find a vertex set of low…
The growing amount of applications that generate vast amount of data in short time scales render the problem of partial monitoring, coupled with prediction, a rather fundamental one. We study the aforementioned canonical problem under the…
Finding large "cliquish" subgraphs is a classic NP-hard graph problem. In this work, we focus on finding maximum $s$-clubs and $s$-plexes, i.e., graphs of diameter $s$ and graphs where each vertex is adjacent to all but $s$ vertices.…
Finding the clique of maximum cardinality in an arbitrary graph is an NP-Hard problem that has many applications, which has motivated studies to solve it exactly despite its difficulty. The great majority of algorithms proposed in the…
The Clique Interdiction Problem (CIP) aims to minimize the size of the largest clique in a given graph by removing a given number of vertices. The CIP models a special Stackelberg game and has important applications in fields such as…