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. © Springer-Verlag Berlin Heidelberg 2000.
CITATION STYLE
Kohayakawa, Y., & Rödl, V. (2000). Algorithmic aspects of regularity. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 1776 LNCS, pp. 1–17). https://doi.org/10.1007/10719839_1
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