Related papers: Streaming PTAS for Binary $\ell_0$-Low Rank Approx…
Piecewise Linear Approximation (PLA) is a well-established tool to reduce the size of the representation of time series by approximating the series by a sequence of line segments while keeping the error introduced by the approximation…
We consider the problem of estimating the value of max cut in a graph in the streaming model of computation. At one extreme, there is a trivial $2$-approximation for this problem that uses only $O(\log n)$ space, namely, count the number of…
For a directed graph $G$ with $n$ vertices and a start vertex $u_{\sf start}$, we wish to (approximately) sample an $L$-step random walk over $G$ starting from $u_{\sf start}$ with minimum space using an algorithm that only makes few passes…
We extend the multi-pass streaming model to sliding window problems, and address the problem of computing order statistics on fixed-size sliding windows, in the multi-pass streaming model as well as the closely related communication…
Motivated by applications in redistricting, we consider the uniform capacitated k-median and uniform capacitated k-means problems in bounded doubling metrics. We provide the first QPTAS for both problems and the first PTAS for the uniform…
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,…
In the $k$-mismatch problem we are given a pattern of length $n$ and a text and must find all locations where the Hamming distance between the pattern and the text is at most $k$. A series of recent breakthroughs have resulted in an…
We study the problem of finding all $k$-periods of a length-$n$ string $S$, presented as a data stream. $S$ is said to have $k$-period $p$ if its prefix of length $n-p$ differs from its suffix of length $n-p$ in at most $k$ locations. We…
We study the communication complexity and streaming complexity of approximating unweighted semi-matchings. A semi-matching in a bipartite graph G = (A, B, E), with n = |A|, is a subset of edges S that matches all A vertices to B vertices…
In this paper, we propose a novel framework that converts streaming algorithms for monotone submodular maximization into streaming algorithms for non-monotone submodular maximization. This reduction readily leads to the currently tightest…
Big data problems frequently require processing datasets in a streaming fashion, either because all data are available at once but collectively are larger than available memory or because the data intrinsically arrive one data point at a…
Clustering of data points in metric space is among the most fundamental problems in computer science with plenty of applications in data mining, information retrieval and machine learning. Due to the necessity of clustering of large…
Tracking and approximating data matrices in streaming fashion is a fundamental challenge. The problem requires more care and attention when data comes from multiple distributed sites, each receiving a stream of data. This paper considers…
The efficient estimation of frequency moments of a data stream in one-pass using limited space and time per item is one of the most fundamental problem in data stream processing. An especially important estimation is to find the number of…
The \emph{$\ell_2$ tracking problem} is the task of obtaining a streaming algorithm that, given access to a stream of items $a_1,a_2,a_3,\ldots$ from a universe $[n]$, outputs at each time $t$ an estimate to the $\ell_2$ norm of the…
In the Palindrome Problem one tries to find all palindromes (palindromic substrings) in a given string. A palindrome is defined as a string which reads forwards the same as backwards, e.g., the string "racecar". A related problem is the…
We study the problem of entrywise $\ell_1$ low rank approximation. We give the first polynomial time column subset selection-based $\ell_1$ low rank approximation algorithm sampling $\tilde{O}(k)$ columns and achieving an…
Extracting latent low-dimensional structure from high-dimensional data is of paramount importance in timely inference tasks encountered with `Big Data' analytics. However, increasingly noisy, heterogeneous, and incomplete datasets as well…
We present the first polynomial-time approximation schemes (PTASes) for the following subset-connectivity problems in edge-weighted graphs of bounded genus: Steiner tree, low-connectivity survivable-network design, and subset TSP. The…
The Consensus Clustering problem has been introduced as an effective way to analyze the results of different microarray experiments. The problem consists of looking for a partition that best summarizes a set of input partitions (each…