2019/04/16 by Robert Krauthgamer, Krauthgamer, Robert, David Reitblat +1 · 1 citation
Computer Science · #Advanced Graph Theory Research #Complexity and Algorithms in Graphs #Data Structures and Algorithms (cs.DS) #Error Correcting Code Techniques #FOS: Computer and information sciences
paper · pdf · doi:10.48550/arxiv.1904.07957
openalex publication_date 2019/04/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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-1log 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.