A deterministic algorithm for summarizing asynchronous streams over a sliding window

Costas Busch, Srikanta Tirthapura

Research output: Chapter in Book/Report/Conference proceedingConference contribution

19 Scopus citations

Abstract

We consider the problem of maintaining aggregates over recent elements of a massive data stream. Motivated by applications involving network data, we consider asynchronous data streams, where the observed order of data may be different from the order in which the data was generated. The set of recent elements is modeled as a sliding timestamp window of the stream, whose elements are changing continuously with time. We present the first deterministic algorithms for maintaining a small space summary of elements in a sliding timestamp window of an asynchronous data stream. The summary can return approximate answers for the following fundamental aggregates: basic count, the number of elements within the sliding window, and sum, the sum of all element values within the sliding window. For basic counting, the space taken by our summary is O(log W · log B · (log W + log B)/ε) bits, where B is an upper bound on the value of the basic count, W is an upper bound on the width of the timestamp window, and e is the desired relative error. Our algorithms are based on a novel data structure called splittable histogram. Prior to this work, randomized algorithms were known for this problem, which provide weaker guarantees than those provided by our deterministic algorithms.

Original languageEnglish (US)
Title of host publicationSTACS 2007 - 24th Annual Symposium on Theoretical Aspects of Computer Science, Proceedings
PublisherSpringer Verlag
Pages465-476
Number of pages12
ISBN (Print)9783540709176
DOIs
StatePublished - 2007
Externally publishedYes
Event24th Annual Symposium on Theoretical Aspects of Computer Science, STACS 2007 - Aachen, Germany
Duration: Feb 22 2007Feb 24 2007

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume4393 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Conference

Conference24th Annual Symposium on Theoretical Aspects of Computer Science, STACS 2007
CountryGermany
CityAachen
Period2/22/072/24/07

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computer Science(all)

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