#### Title

An optimal algorithm for checking regularity (extended abstract)

#### Document Type

Conference Proceeding

#### Date of Original Version

1-1-2002

#### Abstract

We present a deterministic algorithm A that, in 0(m2) time, verifies whether a given m by m bipartite graph G is regular, in the sense of Szemeredi [18]. In the case in which G is not regular enough, our algorithm outputs a vntness to this irregularity. Algorithm A may be used as a subroutine in an algorithm that finds an e-regular partition of a given n-vertex graph Λ in time 0(n2). This time complexity is optimal, up to a constant factor, and improves upon the bound 0(M(n)), proved by Alon, Duke, Lefmann, Rodl, and Yuster [1, 2], where M(n) = 0(n2-376) is the time required to square a 6-1 matrix over the integers. Our approach is elementary, except that it makes use of linear-sized expanders to accomplish a suitable form of deterministic sampling.

#### Publication Title, e.g., Journal

Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms

#### Volume

06-08-January-2002

#### Citation/Publisher Attribution

Kohayakawa, Y., V. Rodl, and L. Thoma.
"An optimal algorithm for checking regularity (extended abstract)."
*Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms*
06-08-January-2002,
(2002): 277-286.
https://digitalcommons.uri.edu/math_facpubs/251