Almost-Smooth Histograms and Sliding-Window Graph Algorithms

@article{Krauthgamer2022AlmostSmoothHA,
title={Almost-Smooth Histograms and Sliding-Window Graph Algorithms},
author={Robert Krauthgamer and David Reitblat},
journal={ArXiv},
year={2022},
volume={abs/1904.07957}
}
• Published 16 April 2019
• Computer Science, Mathematics
• ArXiv
We study algorithms for the sliding-window model, an important variant of the data-stream model, in which the goal is to compute some function of a fixed-length suffix of the stream. We extend the smooth-histogram framework of Braverman and Ostrovsky (FOCS 2007) to almost-smooth functions, which includes all subadditive functions. Specifically, we show that if a subadditive function can be $(1+\epsilon)$-approximated in the insertion-only streaming model, then it can be $(2+\epsilon… 5 Citations Symmetric Norm Estimation and Regression on Sliding Windows • Computer Science, Mathematics COCOON • 2021 This work observes that the symmetric norm streaming algorithm of Braverman et al. (STOC 2017) can be reduced to identifying and approximating the frequency of heavy-hitters in a number of substreams, and introduces a heavy-hitter algorithm that gives a (1 + )-approximation to each of the reported frequencies in the sliding window model. Sliding Window Algorithms for k-Clustering Problems • Computer Science NeurIPS • 2020 This work provides simple and practical algorithms that update the solution efficiently with each arrival rather than recomputing it from scratch, and finds solutions with costs only slightly higher than those returned by algorithms with access to the full dataset. VERTEX COVER IN THE SLIDING WINDOW MODEL • Computer Science, Mathematics • 2021 A (3 + ε ) approximation algorithm for the minimum vertex cover problem in the sliding window model using ˜ O ( n ) space, where ∼ encompasses 1 ε, log n factors with n being the number of vertices in the graph. Maximum-Weight Matching in Sliding Windows and Beyond • Computer Science, Mathematics • 2021 The maximum-weight matching problem in the sliding-window model is studied, and it is shown that given an α-approximation algorithm for a subadditive function f in the insertion-only model the authors can maintain a (2α + ε) approximation of f in this model, which improves upon recent result Krauthgamer and Reitblat [14]. References SHOWING 1-10 OF 30 REFERENCES Maintaining Stream Statistics over Sliding Windows • Computer Science, Mathematics SIAM J. Comput. • 2002 The problem of maintaining aggregates and statistics over data streams, with respect to the last N data elements seen so far, is considered, and it is shown that, using$O(\frac{1}{\epsilon} \log^2 N)$bits of memory, the number of 1's can be estimated to within a factor of$1 + \ep silon$. Dynamic Graphs in the Sliding-Window Model • Computer Science ESA • 2013 An extensive set of positive results including algorithms for constructing basic graph synopses like combinatorial sparsifiers and spanners as well as approximating classic graph properties such as the size of a graph matching or minimum spanning tree are presented. Tight Bounds for Adversarially Robust Streams and Sliding Windows via Difference Estimators • Computer Science 2021 IEEE 62nd Annual Symposium on Foundations of Computer Science (FOCS) • 2022 The results show there is no separation between the sliding window model and the standard data stream model in terms of the approximation factor, and the first difference estimators for a wide range of problems are developed. The Sparse Awakens: Streaming Algorithms for Matching Size Estimation in Sparse Graphs • Computer Science ESA • 2017 Improved streaming algorithms for approximating the size of maximum matching with sparse (bounded arboricity) graphs and the first with an approximation guarantee independent of d are presented. Better Streaming Algorithms for the Maximum Coverage Problem • Computer Science, Mathematics Theory of Computing Systems • 2018 The main goal of this work is to design algorithms, with approximation guarantees as close as possible to 1−1/e$1-1/ e$, that use sublinear space o(mn)$o(mn), and to study the maximum k-vertex coverage problem in the dynamic graph stream model.
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