A deterministic algorithm for the Frieze-Kannan regularity lemma

Authors:
Domingos Dellamonica;Subrahmanyam Kalyanasundaram;Daniel Martin;Vojtěch Rödl;Asaf Shapira
Affiliations:
Department of Mathematics and Computer Science, Emory University, Atlanta, GA;School of Computer Science, Georgia Institute of Technology, Atlanta, GA;Center for Mathematics, Computer Science and Cognition, Universidade Federal do ABC, Santo André, SP, Brazil;Department of Mathematics and Computer Science, Emory University, Atlanta, GA;School of Mathematics and School of Computer Science, Georgia Institute of Technology, Atlanta, GA
Venue:
APPROX'11/RANDOM'11 Proceedings of the 14th international workshop and 15th international conference on Approximation, randomization, and combinatorial optimization: algorithms and techniques
Year:
2011

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Abstract

The Frieze-Kannan regularity lemma is a powerful tool in combinatorics. It has also found applications in the design of approximation algorithms and recently in the design of fast combinatorial algorithms for boolean matrix multiplication. The algorithmic applications of this lemma require one to efficiently construct a partition satisfying the conditions of the lemma. Williams [24] recently asked if one can construct a partition satisfying the conditions of the Frieze-Kannan regularity lemma in deterministic sub-cubic time. We resolve this problem by designing an Õ(nω) time algorithm for constructing such a partition, where ω