Related papers: Simultaneously Approximating All Norms for Massive…
This paper studies the fair range clustering problem in which the data points are from different demographic groups and the goal is to pick $k$ centers with the minimum clustering cost such that each group is at least minimally represented…
Correlation clustering is arguably the most natural formulation of clustering. Given n objects and a pairwise similarity measure, the goal is to cluster the objects so that, to the best possible extent, similar objects are put in the same…
Recently, Hierarchical Clustering (HC) has been considered through the lens of optimization. In particular, two maximization objectives have been defined. Moseley and Wang defined the \emph{Revenue} objective to handle similarity…
Chromatic Correlation Clustering (CCC) generalizes Correlation Clustering by assigning multiple categorical relationships (colors) to edges and imposing chromatic constraints on the clusters. Unlike traditional Correlation Clustering, which…
We study the problem of graph clustering under a broad class of objectives in which the quality of a cluster is defined based on the ratio between the number of edges in the cluster, and the total weight of vertices in the cluster. We show…
We consider a generalized version of the correlation clustering problem, defined as follows. Given a complete graph $G$ whose edges are labeled with $+$ or $-$, we wish to partition the graph into clusters while trying to avoid errors: $+$…
We provide a randomized linear time approximation scheme for a generic problem about clustering of binary vectors subject to additional constrains. The new constrained clustering problem encompasses a number of problems and by solving it,…
We outline a new approach for solving optimization problems which enforce triangle inequalities on output variables. We refer to this as metric-constrained optimization, and give several examples where problems of this form arise in machine…
The fair $k$-median problem is one of the important clustering problems. The current best approximation ratio is 4.675 for this problem with 1-fair violation, which was proposed by Bercea et al. [APPROX-RANDOM'2019]. As far as we know,…
Given a graph with positive and negative edge labels, the correlation clustering problem aims to cluster the nodes so to minimize the total number of between-cluster positive and within-cluster negative edges. This problem has many…
In this paper, we reduce the complexity of approximating the correlation clustering problem from $O(m\times\left( 2+ \alpha (G) \right)+n)$ to $O(m+n)$ for any given value of $\varepsilon$ for a complete signed graph with $n$ vertices and…
With the aggressive scaling of VLSI technology, the explosion of layout patterns creates a critical bottleneck for DFM applications like OPC. Pattern clustering is essential to reduce data complexity, yet existing methods struggle with…
Consensus clustering seeks to combine multiple clusterings of the same dataset, potentially derived by considering various non-sensitive attributes by different agents in a multi-agent environment, into a single partitioning that best…
We initiate the study of trade-offs between sparsity and the number of measurements in sparse recovery schemes for generic norms. Specifically, for a norm $\|\cdot\|$, sparsity parameter $k$, approximation factor $K>0$, and probability of…
In many fundamental combinatorial optimization problems, a feasible solution induces some real cost vectors as an intermediate result, and the optimization objective is a certain function of the vectors. For example, in the problem of…
We present an $(e^{O(p)} \frac{\log \ell}{\log\log\ell})$-approximation algorithm for socially fair clustering with the $\ell_p$-objective. In this problem, we are given a set of points in a metric space. Each point belongs to one (or…
We develop a novel parallel decomposition strategy for unweighted, undirected graphs, based on growing disjoint connected clusters from batches of centers progressively selected from yet uncovered nodes. With respect to similar previous…
Correlation clustering is a technique for aggregating data based on qualitative information about which pairs of objects are labeled 'similar' or 'dissimilar.' Because the optimization problem is NP-hard, much of the previous literature…
The goal of clustering is to group similar objects into meaningful partitions. This process is well understood when an explicit similarity measure between the objects is given. However, far less is known when this information is not readily…
As massive graphs become more prevalent, there is a rapidly growing need for scalable algorithms that solve classical graph problems, such as maximum matching and minimum vertex cover, on large datasets. For massive inputs, several…