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Contemplations on testing graph properties. (English) Zbl 1291.05195
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, 547-554 (2011).
Summary: This article documents two programmatic comments regarding testing graph properties, which I made during the Dagstuhl workshop on Sublinear-Time Algorithms (July 2005). The first comment advocates paying more attention to the dependence of the tester’s complexity on the proximity parameter. The second comment advocates paying more attention to the question of testing general graphs (rather than dense or bounded-degree ones). In addition, this article includes a suggestion to view and discuss property testing within the framework of promise problems.
For the entire collection see [Zbl 1220.68005].

MSC:
05C85 Graph algorithms (graph-theoretic aspects)
68R10 Graph theory (including graph drawing) in computer science
68W20 Randomized algorithms
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