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Algorithmic Aspects of Regularity

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Abstract

Szemerédi’s celebrated regularity lemma proved to be a fundamental result in graph theory. Roughly speaking, his lemma states that any graph may be approximated by a union of a bounded number of bipartite graphs, each of which is ‘pseudorandom’. As later proved by Alon, Duke, Lefmann, Rödl, and Yuster, there is a fast deterministic algorithm for finding such an approximation, and therefore many of the existential results based on the regularity lemma could be turned into constructive results. In this survey, we discuss some recent developments concerning the algorithmic aspects of the regularity lemma.

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Author information

Authors and Affiliations

  1. Instituto de Matemática e Estatística, Universidade de São Paulo, Rua do Matão 1010, 05508-900, São Paulo, Brazil

    Y. Kohayakawa

  2. Department of Mathematics and Computer Science, Emory University, Atlanta, GA, 30322, USA

    V. Rödl

Authors
  1. Y. Kohayakawa
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  2. V. Rödl
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Editors and Affiliations

  1. ETH Zurich, Institute of Computational Science, CH-8092 Zurich and, Swiss Institute of Bioinformatics, Switzerland

    Gaston H. Gonnet

  2. Pedeciba Informática, Casilla de Correo 16120, Distrito 6, Montevideo, Uruguay

    Alfredo Viola

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Kohayakawa, Y., Rödl, V. (2000). Algorithmic Aspects of Regularity. In: Gonnet, G.H., Viola, A. (eds) LATIN 2000: Theoretical Informatics. LATIN 2000. Lecture Notes in Computer Science, vol 1776. Springer, Berlin, Heidelberg. https://doi.org/10.1007/10719839_1

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  • DOI: https://doi.org/10.1007/10719839_1

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  • Print ISBN: 978-3-540-67306-4

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