Related papers: On 2-Clubs in Graph-Based Data Clustering: Theory …
Image segmentation has come a long way since the early days of computer vision, and still remains a challenging task. Modern variations of the classical (purely bottom-up) approach, involve, e.g., some form of user assistance (interactive…
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…
Graph editing problems offer an interesting perspective on sub- and supergraph identification problems for a large variety of target properties. They have also attracted significant attention in recent years, particularly in the area of…
Spectral clustering has become one of the most widely used clustering techniques when the structure of the individual clusters is non-convex or highly anisotropic. Yet, despite its immense popularity, there exists fairly little theory about…
Clustering a graph, i.e., assigning its nodes to groups, is an important operation whose best known application is the discovery of communities in social networks. Graph clustering and community detection have traditionally focused on…
The analysis of several algorithms and data structures can be framed as a peeling process on a random hypergraph: vertices with degree less than k and their adjacent edges are removed until no vertices of degree less than k are left. Often…
Graph clustering, or community detection, is the task of identifying groups of closely related objects in a large network. In this paper we introduce a new community-detection framework called LambdaCC that is based on a specially weighted…
In this paper we study the problem of correlation clustering under fairness constraints. In the classic correlation clustering problem, we are given a complete graph where each edge is labeled positive or negative. The goal is to obtain a…
Graph clustering is a fundamental problem that has been extensively studied both in theory and practice. The problem has been defined in several ways in literature and most of them have been proven to be NP-Hard. Due to their high practical…
In the Vertex Cover Reconfiguration (VCR) problem, given a graph $G$, positive integers $k$ and $\ell$ and two vertex covers $S$ and $T$ of $G$ of size at most $k$, we determine whether $S$ can be transformed into $T$ by a sequence of at…
Circular layouts are a popular graph drawing style, where vertices are placed on a circle and edges are drawn as straight chords. Crossing minimization in circular layouts is \NP-hard. One way to allow for fewer crossings in practice are…
A 2-packing set for an undirected, weighted graph G=(V,E,w) is a subset S of the vertices V such that any two vertices are not adjacent and have no common neighbors. The Maximum Weight 2-Packing Set problem that asks for a 2-packing set of…
In the Online Delayed Connected H-Node-Deletion Problem, an unweighted graph is revealed vertex by vertex and it must remain free of any induced copies of a specific connected induced forbidden subgraph H at each point in time. To achieve…
One of the most useful measures of cluster quality is the modularity of a partition, which measures the difference between the number of the edges joining vertices from the same cluster and the expected number of such edges in a random…
Given a graph $G$ and a positive integer $k$, the 2-Load coloring problem is to check whether there is a $2$-coloring $f:V(G) \rightarrow \{r,b\}$ of $G$ such that for every $i \in \{r,b\}$, there are at least $k$ edges with both end…
Convex clustering has recently garnered increasing interest due to its attractive theoretical and computational properties, but its merits become limited in the face of high-dimensional data. In such settings, pairwise affinity terms that…
For a fixed graph $H$, the $H$-free-editing problem asks whether we can modify a given graph $G$ by adding or deleting at most $k$ edges such that the resulting graph does not contain $H$ as an induced subgraph. The problem is known to be…
Graph clustering involves the task of dividing nodes into clusters, so that the edge density is higher within clusters as opposed to across clusters. A natural, classic and popular statistical setting for evaluating solutions to this…
A recent trend in data mining has explored (hyper)graph clustering algorithms for data with categorical relationship types. Such algorithms have applications in the analysis of social, co-authorship, and protein interaction networks, to…
Graph is a ubiquitous data structure in data science that is widely applied in social networks, knowledge representation graphs, recommendation systems, etc. When given a graph dataset consisting of one graph or more graphs, where the…