An algorithmic regularity lemma for $L_p$ regular sparse matrices

Abstract

We prove an algorithmic regularity lemma for $L_p$ regular matrices $(1<p\le \infty ),$ a class of sparse $\{0,1\}$ matrices which obey a natural pseudorandomness condition. This extends a result of Coja-Oghlan, Cooper and Frieze who treated the case of $L_{\infty }$ regular matrices. We also present applications of this result for tensors and MAX-CSP instances.