An optimal algorithm for the distinct elements problem

DM Kane, J Nelson, DP Woodruff - Proceedings of the twenty-ninth ACM …, 2010 - dl.acm.org
We give the first optimal algorithm for estimating the number of distinct elements in a data
stream, closing a long line of theoretical research on this problem begun by Flajolet and …

The white-box adversarial data stream model

M Ajtai, V Braverman, TS Jayram, S Silwal… - Proceedings of the 41st …, 2022 - dl.acm.org
There has been a flurry of recent literature studying streaming algorithms for which the input
stream is chosen adaptively by a black-box adversary who observes the output of the …

Small-space and streaming pattern matching with edits

T Kociumaka, E Porat… - 2021 IEEE 62nd Annual …, 2022 - ieeexplore.ieee.org
In this work, we revisit the fundamental and well-studied problem of approximate pattern
matching under edit distance. Given an integer k, a pattern P of length m, and a text T of …

Optimal lower bounds for universal relation, and for samplers and finding duplicates in streams

M Kapralov, J Nelson, J Pachocki… - 2017 IEEE 58th …, 2017 - ieeexplore.ieee.org
In the communication problem UR (universal relation)[25], Alice and Bob respectively
receive x, y∈{0, 1} n with the promise that x≠ y. The last player to receive a message must …

A (1+ ln2)-approximation algorithm for minimum-cost 2-edge-connectivity augmentation of trees with constant radius

N Cohen, Z Nutov - Theoretical Computer Science, 2013 - Elsevier
We consider the Tree Augmentation problem: given a graph G=(V, E) with edge-costs and a
tree T on V disjoint to E, find a minimum-cost edge-subset F⊆ E such that T∪ F is 2-edge …

The k-mismatch problem revisited

R Clifford, A Fontaine, E Porat, B Sach… - Proceedings of the twenty …, 2016 - SIAM
We revisit the complexity of one of the most basic problems in pattern matching. In the k-
mismatch problem we must compute the Hamming distance between a pattern of length m …

The streaming k-mismatch problem

R Clifford, T Kociumaka, E Porat - Proceedings of the Thirtieth Annual ACM …, 2019 - SIAM
We consider the streaming complexity of a fundamental task in approximate pattern
matching: the k-mismatch problem. In this problem, we must compute Hamming distances …

Real-time streaming string-matching

D Breslauer, Z Galil - ACM Transactions on Algorithms (TALG), 2014 - dl.acm.org
This article presents a real-time randomized streaming string-matching algorithm that uses O
(log m) space. The algorithm only makes one-sided small probability false-positive errors …

An Optimal Algorithm for ℓ1-Heavy Hitters in Insertion Streams and Related Problems

A Bhattacharyya, P Dey, DP Woodruff - ACM Transactions on Algorithms …, 2018 - dl.acm.org
We give the first optimal bounds for returning the ℓ1-heavy hitters in a data stream of
insertions, together with their approximate frequencies, closing a long line of work on this …

Dictionary matching in a stream

R Clifford, A Fontaine, E Porat, B Sach… - Algorithms-ESA 2015 …, 2015 - Springer
We consider the problem of dictionary matching in a stream. Given a set of strings, known as
a dictionary, and a stream of characters arriving one at a time, the task is to report each time …