The sparse awakens: Streaming algorithms for matching size estimation in sparse graphs

Graham Cormode, Hossein Jowhari, Morteza Monemizadeh, S. Muthukrishnan

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

    Abstract

    Estimating the size of the maximum matching is a canonical problem in graph analysis, and one that has attracted extensive study over a range of different computational models. We present improved streaming algorithms for approximating the size of maximum matching with sparse (bounded arboricity) graphs. (Insert-Only Streams) We present a one-pass algorithm that takes O(α log n) space and approximates the size of the maximum matching in graphs with arboricity α within a factor of O(α). This improves significantly upon the state-of-The-Art Õ(α n2/3)-space streaming algorithms, and is the first poly-logarithmic space algorithm for this problem. (Dynamic Streams) Given a dynamic graph stream (i.e., inserts and deletes) of edges of an underlying α -bounded arboricity graph, we present an one-pass algorithm that uses space Õ(α 10/3n2/3) and returns an O(α)-estimator for the size of the maximum matching on the condition that the number edge deletions in the stream is bounded by O(α n). For this class of inputs, our algorithm improves the state-of-The-Art O (α n4/5)-space algorithms, where the O (.) notation hides logarithmic in n dependencies. In contrast to prior work, our results take more advantage of the streaming access to the input and characterize the matching size based on the ordering of the edges in the stream in addition to the degree distributions and structural properties of the sparse graphs.

    Original languageEnglish (US)
    Title of host publication25th European Symposium on Algorithms, ESA 2017
    EditorsChristian Sohler, Christian Sohler, Kirk Pruhs
    PublisherSchloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing
    ISBN (Electronic)9783959770491
    DOIs
    StatePublished - Sep 1 2017
    Event25th European Symposium on Algorithms, ESA 2017 - Vienna, Austria
    Duration: Sep 4 2017Sep 6 2017

    Publication series

    NameLeibniz International Proceedings in Informatics, LIPIcs
    Volume87
    ISSN (Print)1868-8969

    Conference

    Conference25th European Symposium on Algorithms, ESA 2017
    CountryAustria
    CityVienna
    Period9/4/179/6/17

    Keywords

    • Matching size
    • Streaming algorithms

    ASJC Scopus subject areas

    • Software

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  • Cite this

    Cormode, G., Jowhari, H., Monemizadeh, M., & Muthukrishnan, S. (2017). The sparse awakens: Streaming algorithms for matching size estimation in sparse graphs. In C. Sohler, C. Sohler, & K. Pruhs (Eds.), 25th European Symposium on Algorithms, ESA 2017 [29] (Leibniz International Proceedings in Informatics, LIPIcs; Vol. 87). Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing. https://doi.org/10.4230/LIPIcs.ESA.2017.29