# 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} }

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, MathematicsCOCOON
- 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 ScienceNeurIPS
- 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.

Smoothness of Schatten Norms and Sliding-Window Matrix Streams

- Computer ScienceInf. Process. Lett.
- 2022

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].

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