An algorithmic regularity lemma for L_p regular sparse matrices

We prove an algorithmic regularity lemma for $L_p$ regular matrices $(1 < p \leq \infty),$ 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.