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This paper presents an algorithm for estimating the weight of a maximum weighted matching by augmenting any estimation routine for the size of an unweighted matching. The algorithm is implementable in any streaming model including dynamic graph streams. We also give the first constant estimation for the maximum matching size in a dynamic graph stream for planar graphs (or any graph with bounded arboricity) using $tilde{O}(n^{4/5})$ space which also extends to weighted matching. Using previous results by Kapralov, Khanna, and Sudan (2014) we obtain a $mathrm{polylog}(n)$ approximation for general graphs using $mathrm{polylog}(n)$ space in random order streams, respectively. In addition, we give a space lower bound of $Omega(n^{1-varepsilon})$ for any randomized algorithm estimating the size of a maximum matching up to a $1+O(varepsilon)$ factor for adversarial streams.
The Jaccard index is an important similarity measure for item sets and Boolean data. On large datasets, an exact similarity computation is often infeasible for all item pairs both due to time and space constraints, giving rise to faster approximate m
We present data streaming algorithms for the $k$-median problem in high-dimensional dynamic geometric data streams, i.e. streams allowing both insertions and deletions of points from a discrete Euclidean space ${1, 2, ldots Delta}^d$. Our algorithms
We present a framework for deterministically rounding a dynamic fractional matching. Applying our framework in a black-box manner on top of existing fractional matching algorithms, we derive the following new results: (1) The first deterministic algo
We present the first single pass algorithm for computing spectral sparsifiers of graphs in the dynamic semi-streaming model. Given a single pass over a stream containing insertions and deletions of edges to a graph G, our algorithm maintains a random
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 need to be