Combinatorica
Matrix multiplication via arithmetic progressions
Journal of Symbolic Computation - Special issue on computational algebraic complexity
Estimating the largest eigenvalues by the power and Lanczos algorithms with a random start
SIAM Journal on Matrix Analysis and Applications
The algorithmic aspects of the regularity lemma
Journal of Algorithms
A Fast Approximation Algorithm for Computing theFrequencies of Subgraphs in a Given Graph
SIAM Journal on Computing
The regularity lemma and its applications in graph theory
Theoretical aspects of computer science
The regularity lemma and approximation schemes for dense problems
FOCS '96 Proceedings of the 37th Annual Symposium on Foundations of Computer Science
An Optimal Algorithm for Checking Regularity
SIAM Journal on Computing
Quasirandomness, Counting and Regularity for 3-Uniform Hypergraphs
Combinatorics, Probability and Computing
Approximating the Cut-Norm via Grothendieck's Inequality
SIAM Journal on Computing
Regularity Lemmas and Combinatorial Algorithms
FOCS '09 Proceedings of the 2009 50th Annual IEEE Symposium on Foundations of Computer Science
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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. R. Williams recently asked if one can construct a partition satisfying the conditions of the Frieze-Kannan regularity lemma in deterministic subcubic time. We resolve this problem by designing an $\tilde O(n^{\omega})$ time algorithm for constructing such a partition, where $\omega