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Almost-Smooth Histograms and Sliding-Window Graph Algorithms.
- Source :
-
Algorithmica . Oct2022, Vol. 84 Issue 10, p2926-2953. 28p. - Publication Year :
- 2022
-
Abstract
- 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 + ε -approximated in the insertion-only streaming model, then it can be 2 + ε -approximated also in the sliding-window model with space complexity larger by factor O ε - 1 log w , where w is the window size. We demonstrate how our framework yields new approximation algorithms with relatively little effort for a variety of problems that do not admit the smooth-histogram technique. For example, in the frequency-vector model, a symmetric norm is subadditive and thus we obtain a sliding-window 2 + ε -approximation algorithm for it. Another example is for streaming matrices, where we derive a new sliding-window 2 + ε -approximation algorithm for Schatten 4-norm. We then consider graph streams and show that many graph problems are subadditive, including maximum submodular matching, minimum vertex-cover, and maximum k-cover, thereby deriving sliding-window O 1 -approximation algorithms for them almost for free (using known insertion-only algorithms). Finally, we design for every d ∈ 1 , 2 an artificial function, based on the maximum-matching size, whose almost-smoothness parameter is exactly d. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 01784617
- Volume :
- 84
- Issue :
- 10
- Database :
- Academic Search Index
- Journal :
- Algorithmica
- Publication Type :
- Academic Journal
- Accession number :
- 159441263
- Full Text :
- https://doi.org/10.1007/s00453-022-00988-y