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Testing graph blow-up. (English) Zbl 1343.68286
Goldreich, Oded (ed.), Studies in complexity and cryptography. Miscellanea on the interplay between randomness and computation. In collaboration with Lidor Avigad, Mihir Bellare, Zvika Brakerski, Shafi Goldwasser, Shai Halevi, Tali Kaufman, Leonid Levin, Noam Nisan, Dana Ron, Madhu Sudan, Luca Trevisan, Salil Vadhan, Avi Wigderson, David Zuckerman. Berlin: Springer (ISBN 978-3-642-22669-4/pbk). Lecture Notes in Computer Science 6650, 156-172 (2011).
Summary: 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 \(\widetilde{O}(1 / \epsilon )\) that distinguishes graphs that are a blow-up of \(H\) from graphs that are \(\epsilon \)-far from any such blow-up.
For the entire collection see [Zbl 1220.68005].

MSC:
68W20 Randomized algorithms
05C50 Graphs and linear algebra (matrices, eigenvalues, etc.)
05C85 Graph algorithms (graph-theoretic aspects)
68Q25 Analysis of algorithms and problem complexity
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