Testing graph blow-up

Abstract

Referring to the query complexity of testing graph properties in the adjacency matrix model, we advance the study of the class of properties that can be tested non-adaptively within complexity that is inversely proportional to the proximity parameter. Arguably, this is the lowest meaningful complexity class in this model, and we show that it contains a very natural class of graph properties. Specifically, for every fixed graph H, we consider the set of all graphs that are obtained by a (possibly unbalanced) blow-up of H. We show a non-adaptive tester of query complexity ̃(1 / ε) that distinguishes graphs that are a blow-up of H from graphs that are ε-far from any such blow-up. © 2011 Springer-Verlag Berlin Heidelberg.