Published online by Cambridge University Press: 03 May 2019
We provide a deterministic algorithm that finds, in ɛ-O(1)n2 time, an ɛ-regular Frieze–Kannan partition of a graph on n vertices. The algorithm outputs an approximation of a given graph as a weighted sum of ɛ-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 ɛnv(H), in time ɛ-OH(1)n2.
J. Fox is supported by a Packard Fellowship, by NSF CAREER award DMS 1352121, and by an Alfred P. Sloan Fellowship.
L. M. Lovász is supported by NSF Postdoctoral Fellowship Award DMS 1705204.
Y. Zhao is supported by NSF awards DMS-1362326 and DMS-1764176, and the MIT Solomon Buchsbaum Fund.
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