Related papers: Clustered Planarity with Pipes
Many datasets take the form of a bipartite graph where two types of nodes are connected by relationships, like the movies watched by a user or the tags associated with a file. The partitioning of the bipartite graph could be used to fasten…
We obtain new examples and the complete list of the rational cuspidal plane curves $C$ with at least three cusps, one of which has multiplicity ${\rm deg}\,C - 2$. It occurs that these curves are projectively rigid. We also discuss the…
We construct a method by which we can calculate the precision with which an algorithm identifies the shape of a cluster. We present our results for several well known clustering algorithms and suggest ways to improve performance for newer…
The problem of finding clusters in complex networks has been extensively studied by mathematicians, computer scientists and, more recently, by physicists. Many of the existing algorithms partition a network into clear clusters, without…
For a clustered graph, i.e, a graph whose vertex set is recursively partitioned into clusters, the C-Planarity Testing problem asks whether it is possible to find a planar embedding of the graph and a representation of each cluster as a…
Clustering is a fundamental tool for analyzing large data sets. A rich body of work has been devoted to designing data-stream algorithms for the relevant optimization problems such as $k$-center, $k$-median, and $k$-means. Such algorithms…
Clustering is one of the most fundamental tools in data science and machine learning, and k-means clustering is one of the most common such methods. There is a variety of approximate algorithms for the k-means problem, but computing the…
Community detection, which focuses on clustering nodes or detecting communities in (mostly) a single network, is a problem of considerable practical interest and has received a great deal of attention in the research community. While being…
We study the generalization of Correlation Clustering which incorporates fairness constraints via the notion of fairlets. The corresponding Fair Correlation Clustering problem has been studied from several perspectives to date, but has so…
In this paper we introduce an algorithm of construction of cyclic space-filling curves. One particular construction provides a family of space-filling curves in all dimensions (H-curves). They are compared here with the Hilbert curve in the…
Correlation clustering is a widely-used approach for clustering large data sets based only on pairwise similarity information. In recent years, there has been a steady stream of better and better classical algorithms for approximating this…
We consider the problem of correlation clustering on graphs with constraints on both the cluster sizes and the positive and negative weights of edges. Our contributions are twofold: First, we introduce the problem of correlation clustering…
Correlation clustering is a central topic in unsupervised learning, with many applications in ML and data mining. In correlation clustering, one receives as input a signed graph and the goal is to partition it to minimize the number of…
In the leader-follower approach, one or more agents are selected as leaders who do not change their states or have autonomous dynamics and can influence other agents, while the other agents, called followers, perform a simple protocol based…
The clustering of a data set is one of the core tasks in data analytics. Many clustering algorithms exhibit a strong contrast between a favorable performance in practice and bad theoretical worst-cases. Prime examples are least-squares…
Clustering is often a challenging problem because of the inherent ambiguity in what the "correct" clustering should be. Even when the number of clusters $K$ is known, this ambiguity often still exists, particularly when there is variation…
Two planar sets are circularly separable if there exists a circle enclosing one of the sets and whose open interior disk does not intersect the other set. This paper studies two problems related to circular separability. A linear-time…
Clustering large, mixed data is a central problem in data mining. Many approaches adopt the idea of k-means, and hence are sensitive to initialisation, detect only spherical clusters, and require a priori the unknown number of clusters. We…
Graphs are used in many disciplines to model the relationships that exist between objects in a complex discrete system. Researchers may wish to compare a network of interest to a "typical" graph from a family (or ensemble) of graphs which…
We present a new model for hybrid planarity that relaxes existing hybrid representations. A graph $G = (V,E)$ is $(k,p)$-planar if $V$ can be partitioned into clusters of size at most $k$ such that $G$ admits a drawing where: (i) each…