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 \(\widetilde{O}\) (1 / ε) that distinguishes graphs that are a blow-up of H from graphs that are ε-far from any such blow-up.
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Avigad, L., Goldreich, O. (2011). Testing Graph Blow-Up. In: Goldreich, O. (eds) Studies in Complexity and Cryptography. Miscellanea on the Interplay between Randomness and Computation. Lecture Notes in Computer Science, vol 6650. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-22670-0_18
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DOI: https://doi.org/10.1007/978-3-642-22670-0_18
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