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… 
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