Related papers: Incremental (k, z)-Clustering on Graphs
In this paper we give the first efficient algorithms for the $k$-center problem on dynamic graphs undergoing edge updates. In this problem, the goal is to partition the input into $k$ sets by choosing $k$ centers such that the maximum…
Given points from an arbitrary metric space and a sequence of point updates sent by an adversary, what is the minimum recourse per update (i.e., the minimum number of changes needed to the set of centers after an update), in order to…
We study the consistent k-center clustering problem. In this problem, the goal is to maintain a constant factor approximate $k$-center solution during a sequence of $n$ point insertions and deletions while minimizing the recourse, i.e., the…
We consider the well-studied Robust $(k, z)$-Clustering problem, which generalizes the classic $k$-Median, $k$-Means, and $k$-Center problems. Given a constant $z\ge 1$, the input to Robust $(k, z)$-Clustering is a set $P$ of $n$ weighted…
Given an undirected graph on a node set $V$ and positive integers $k$ and $m$, a $k$-connected $m$-dominating set ($(k,m)$-CDS) is defined as a subset $S$ of $V$ such that each node in $V \setminus S$ has at least $m$ neighbors in $S$, and…
We study two generalizations of classic clustering problems called dynamic ordered $k$-median and dynamic $k$-supplier, where the points that need clustering evolve over time, and we are allowed to move the cluster centers between…
Partitioning a graph into groups of vertices such that those within each group are more densely connected than vertices assigned to different groups, known as graph clustering, is often used to gain insight into the organisation of large…
The clustering problem, in its many variants, has numerous applications in operations research and computer science (e.g., in applications in bioinformatics, image processing, social network analysis, etc.). As sizes of data sets have grown…
Spectral clustering has become a popular technique due to its high performance in many contexts. It comprises three main steps: create a similarity graph between N objects to cluster, compute the first k eigenvectors of its Laplacian matrix…
Given a sequence of adversarial point insertions and point deletions, is it possible to simultaneously optimize the approximation ratio, update time, and recourse for a $k$-clustering problem? If so, can this be achieved with worst-case…
Given a collection of $n$ points in $\mathbb{R}^d$, the goal of the $(k,z)$-clustering problem is to find a subset of $k$ "centers" that minimizes the sum of the $z$-th powers of the Euclidean distance of each point to the closest center.…
Graph clustering is a fundamental technique in data analysis with applications in many different fields. While there is a large body of work on clustering undirected graphs, the problem of clustering directed graphs is much less understood.…
We developed a flexible parallel algorithm for graph summarization based on vertex-centric programming and parameterized message passing. The base algorithm supports infinitely many structural graph summary models defined in a formal…
We consider the (exact, minimum) $k$-cut problem: given a graph and an integer $k$, delete a minimum-weight set of edges so that the remaining graph has at least $k$ connected components. This problem is a natural generalization of the…
Connected clustering denotes a family of constrained clustering problems in which we are given a distance metric and an undirected connectivity graph $G$ that can be completely unrelated to the metric. The aim is to partition the $n$…
The $k$-center problem is a central optimization problem with numerous applications for machine learning, data mining, and communication networks. Despite extensive study in various scenarios, it surprisingly has not been thoroughly…
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…
Center-based clustering techniques are fundamental in some areas of machine learning such as data summarization. Generic $k$-center algorithms can produce biased cluster representatives so there has been a recent interest in fair $k$-center…
This paper studies clustering algorithms for dynamically evolving graphs $\{G_t\}$, in which new edges (and potential new vertices) are added into a graph, and the underlying cluster structure of the graph can gradually change. The paper…
We study the problem of graph clustering where the goal is to partition a graph into clusters, i.e. disjoint subsets of vertices, such that each cluster is well connected internally while sparsely connected to the rest of the graph. In…