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Buffered Count-Min Sketch on SSD: Theory and Experiments

Authors Mayank Goswami, Dzejla Medjedovic, Emina Mekic, Prashant Pandey



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Author Details

Mayank Goswami
  • Queens College, City University of New York
Dzejla Medjedovic
  • International University of Sarajevo
Emina Mekic
  • Sarajevo School of Science and Technology
Prashant Pandey
  • Stony Brook University, New York

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Mayank Goswami, Dzejla Medjedovic, Emina Mekic, and Prashant Pandey. Buffered Count-Min Sketch on SSD: Theory and Experiments. In 26th Annual European Symposium on Algorithms (ESA 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 112, pp. 41:1-41:15, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2018)
https://doi.org/10.4230/LIPIcs.ESA.2018.41

Abstract

Frequency estimation data structures such as the count-min sketch (CMS) have found numerous applications in databases, networking, computational biology and other domains. Many applications that use the count-min sketch process massive and rapidly evolving data sets. For data-intensive applications that aim to keep the overestimate error low, the count-min sketch becomes too large to store in available RAM and may have to migrate to external storage (e.g., SSD.) Due to the random-read/write nature of hash operations of the count-min sketch, simply placing it on SSD stifles the performance of time-critical applications, requiring about 4-6 random reads/writes to SSD per estimate (lookup) and update (insert) operation. In this paper, we expand on the preliminary idea of the buffered count-min sketch (BCMS) {[Eydi et al., 2017]}, an SSD variant of the count-min sketch, that uses hash localization to scale efficiently out of RAM while keeping the total error bounded. We describe the design and implementation of the buffered count-min sketch, and empirically show that our implementation achieves 3.7 x-4.7 x speedup on update and 4.3 x speedup on estimate operations compared to the traditional count-min sketch on SSD. Our design also offers an asymptotic improvement in the external-memory model over the original data structure: r random I/Os are reduced to 1 I/O for the estimate operation. For a data structure that uses k blocks on SSD, w as the word/counter size, r as the number of rows, M as the number of bits in the main memory, our data structure uses kwr/M amortized I/Os for updates, or, if kwr/M > 1, 1 I/O in the worst case. In typical scenarios, kwr/M is much smaller than 1. This is in contrast to O(r) I/Os incurred for each update in the original data structure. Lastly, we mathematically show that for the buffered count-min sketch, the error rate does not substantially degrade over the traditional count-min sketch. Specifically, we prove that for any query q, our data structure provides the guarantee: Pr[Error(q) >= n epsilon (1+o(1))] <= delta + o(1), which, up to o(1) terms, is the same guarantee as that of a traditional count-min sketch.

Subject Classification

ACM Subject Classification
  • Theory of computation → Data structures and algorithms for data management
  • Theory of computation → Streaming models
  • Theory of computation → Database query processing and optimization (theory)
Keywords
  • Streaming model
  • Count-min sketch
  • Counting
  • Frequency
  • External memory
  • I/O efficiency
  • Bloom filter
  • Counting filter
  • Quotient filter

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