Related papers: A $(3+\varepsilon)$-Approximate Correlation Cluste…

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…

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…

We combine several recent advancements to solve $(1+\varepsilon)$-transshipment and $(1+\varepsilon)$-maximum flow with a parallel algorithm with $\tilde{O}(1/\varepsilon)$ depth and $\tilde{O}(m/\varepsilon)$ work. We achieve this by…

We present the first semi-streaming PTAS for the minimum feedback arc set problem on directed tournaments in a small number of passes. Namely, we obtain a $(1 + \varepsilon)$-approximation in polynomial time $O \left( \text{poly}(n)…

Several clustering frameworks with interactive (semi-supervised) queries have been studied in the past. Recently, clustering with same-cluster queries has become popular. An algorithm in this setting has access to an oracle with full…

We show that both clustering and subspace embeddings can be performed in the streaming model with the same asymptotic efficiency as in the central/offline setting. For $(k, z)$-clustering in the streaming model, we achieve a number of words…

We present a parallel algorithm for the $(1-\epsilon)$-approximate maximum flow problem in capacitated, undirected graphs with $n$ vertices and $m$ edges, achieving $O(\epsilon^{-3}\text{polylog} n)$ depth and $O(m \epsilon^{-3}…

Approximate computing aims for efficient execution of workflows where an approximate output is sufficient instead of the exact output. The idea behind approximate computing is to compute over a representative sample instead of the entire…

In this paper, we study the problem of learning a mixture of Gaussians with streaming data: given a stream of $N$ points in $d$ dimensions generated by an unknown mixture of $k$ spherical Gaussians, the goal is to estimate the model…

Given a similarity graph between items, correlation clustering (CC) groups similar items together and dissimilar ones apart. One of the most popular CC algorithms is KwikCluster: an algorithm that serially clusters neighborhoods of…

This paper studies density-based clustering of point sets. These methods use dense regions of points to detect clusters of arbitrary shapes. In particular, we study variants of density peaks clustering, a popular type of algorithm that has…

Data stream clustering is a critical operation in various real-world applications, ranging from the Internet of Things (IoT) to social media and financial systems. Existing data stream clustering algorithms, while effective to varying…

A technique introduced by Indyk and Woodruff [STOC 2005] has inspired several recent advances in data-stream algorithms. We show that a number of these results follow easily from the application of a single probabilistic method called…

Problems involving the efficient arrangement of simple objects, as captured by bin packing and makespan scheduling, are fundamental tasks in combinatorial optimization. These are well understood in the traditional online and offline cases,…

Core-sets refer to subsets of data that maximize some function that is commonly a diversity or group requirement. These subsets are used in place of the original data to accomplish a given task with comparable or even enhanced performance…

The number of triangles is a computationally expensive graph statistic which is frequently used in complex network analysis (e.g., transitivity ratio), in various random graph models (e.g., exponential random graph model) and in important…

Online structure learning approaches, such as those stemming from Statistical Relational Learning, enable the discovery of complex relations in noisy data streams. However, these methods assume the existence of fully-labelled training data,…

Given a complete graph $G = (V, E)$ where each edge is labeled $+$ or $-$, the Correlation Clustering problem asks to partition $V$ into clusters to minimize the number of $+$edges between different clusters plus the number of $-$edges…

We provide the first streaming algorithm for computing a provable approximation to the $k$-means of sparse Big data. Here, sparse Big Data is a set of $n$ vectors in $\mathbb{R}^d$, where each vector has $O(1)$ non-zeroes entries, and…

Recently, considerable efforts have been devoted to approximately computing the global and local (i.e., incident to each node) triangle counts of a large graph stream represented as a sequence of edges. Existing approximate triangle…