Related papers: Listing All Maximal Cliques in Large Sparse Real-W…
A $k$-defective clique of an undirected graph $G$ is a subset of its vertices that induces a nearly complete graph with a maximum of $k$ missing edges. The maximum $k$-defective clique problem, which asks for the largest $k$-defective…
In this paper, we provide polynomial-time algorithms for different extensions of the matching counting problem, namely maximal matchings, path matchings (linear forest) and paths, on graph classes of bounded clique-width. For maximal…
We consider the problem of finding a large clique in an Erd\H{o}s--R\'enyi random graph where we are allowed unbounded computational time but can only query a limited number of edges. Recall that the largest clique in $G \sim G(n,1/2)$ has…
Sparsity-constrained optimization is an important and challenging problem that has wide applicability in data mining, machine learning, and statistics. In this paper, we focus on sparsity-constrained optimization in cases where the cost…
A set of vertices in a graph forms a potential maximal clique if there exists a minimal chordal completion in which it is a maximal clique. Potential maximal cliques were first introduced as a key tool to obtain an efficient, though…
We present an exact algorithm for computing all common subgraphs with the maximum number of vertices across multiple graphs. Our approach is further extended to handle the connected Maximum Common Subgraph (MCS), identifying the largest…
A strong clique in a graph is a clique intersecting every maximal independent set. We study the computational complexity of six algorithmic decision problems related to strong cliques in graphs and almost completely determine their…
Dynamics of interactions play an increasingly important role in the analysis of complex networks. A modeling framework to capture this are temporal graphs which consist of a set of vertices (entities in the network) and a set of…
Mining cohesive subgraphs from a graph is a fundamental problem in graph data analysis. One notable cohesive structure is $\gamma$-quasi-clique (QC), where each vertex connects at least a fraction $\gamma$ of the other vertices inside.…
We present CLIPPER+, an algorithm for finding maximal cliques in unweighted graphs for outlier-robust global registration. The registration problem can be formulated as a graph and solved by finding its maximum clique. This formulation…
Many real-world networks, such as transportation or trade networks, are dynamic in the sense that the edge set may change over time, but these changes are known in advance. This behavior is captured by the temporal graphs model, which has…
We introduce a new distributed algorithm for aligning graphs or finding substructures within a given graph. It is based on the cavity method and is used to study the maximum-clique and the graph-alignment problems in random graphs. The…
A graph is said to be well-covered if all its maximal independent sets are of the same size. In 1999, Yamashita and Kameda introduced a subclass of well-covered graphs, called localizable graphs and defined as graphs having a partition of…
We consider the maintenance of the set of all maximal cliques in a dynamic graph that is changing through the addition or deletion of edges. We present nearly tight bounds on the magnitude of change in the set of maximal cliques, as well as…
A canonical problem in graph mining is the detection of dense communities. This problem is exacerbated for a graph with a large order and size -- the number of vertices and edges -- as many community detection algorithms scale poorly. In…
Many algorithms have been proposed for detecting disjoint communities (relatively densely connected subgraphs) in networks. One popular technique is to optimize modularity, a measure of the quality of a partition in terms of the number of…
While algebrisation constitutes a powerful technique in the design and analysis of centralised algorithms, to date there have been hardly any applications of algebraic techniques in the context of distributed graph algorithms. This work is…
We introduce a new algorithmic framework for designing dynamic graph algorithms in minor-free graphs, by exploiting the structure of such graphs and a tool called vertex sparsification, which is a way to compress large graphs into small…
This manuscript provides a comprehensive review of the Maximum Clique Problem, a computational problem that involves finding subsets of vertices in a graph that are all pairwise adjacent to each other. The manuscript covers in a simple way…
Estimating the size of the maximum matching is a canonical problem in graph algorithms, and one that has attracted extensive study over a range of different computational models. We present improved streaming algorithms for approximating…