A fast new algorithm for weak graph regularity

Abstract

We provide a deterministic algorithm that finds, in ϵ-O(1) n 2 time, an ϵ-regular Frieze-Kannan partition of a graph on n vertices. The algorithm outputs an approximation of a given graph as a weighted sum of ϵ-O(1) many complete bipartite graphs. As a corollary, we give a deterministic algorithm for estimating the number of copies of H in an n-vertex graph G up to an additive error of at most ϵn v(H), in time ϵ-O H(1) n 2