A characterization of testable hypergraph properties

Felix Joos; Jaehoon Kim; Daniela Kuhn; Deryk Osthus

doi:10.1109/FOCS.2017.84

A characterization of testable hypergraph properties

Felix Joos^*, Jaehoon Kim, Daniela Kuhn, Deryk Osthus

^*Corresponding author for this work

Mathematics

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

3 Citations (Scopus)

141 Downloads (Pure)

Abstract

We provide a combinatorial characterization of all testable properties of k-graphs (i.e. k-uniform hypergraphs). Here, a k-graph property P is testable if there is a randomized algorithm which makes a bounded number of edge queries and distinguishes with probability 2/3 between k-graphs that satisfy P and those that are far from satisfying P. For the 2-graph case, such a combinatorial characterization was obtained by Alon, Fischer, Newman and Shapira. Our results for the k-graph setting are in contrast to those of Austin and Tao, who showed that for the somewhat stronger concept of local repairability, the testability results for graphs do not extend to the 3-graph setting.

Original language	English
Title of host publication	Proceedings - 58th Annual IEEE Symposium on Foundations of Computer Science, FOCS 2017
Publisher	IEEE Computer Society Press
Pages	859-867
Number of pages	9
Volume	2017-October
ISBN (Electronic)	9781538634646
DOIs	https://doi.org/10.1109/FOCS.2017.84
Publication status	Published - 13 Nov 2017
Event	58th Annual IEEE Symposium on Foundations of Computer Science, FOCS 2017 - Berkeley, United States Duration: 15 Oct 2017 → 17 Oct 2017

Conference

Conference	58th Annual IEEE Symposium on Foundations of Computer Science, FOCS 2017
Country/Territory	United States
City	Berkeley
Period	15/10/17 → 17/10/17

Keywords

hypergraphs
property testing
regularity lemma

ASJC Scopus subject areas

Computer Science(all)

Access to Document

10.1109/FOCS.2017.84

property_testing_conference2
Checked for eligibility: 20/02/2018
Accepted author manuscript, 362 KB

https://arxiv.org/abs/1707.03303

Cite this

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title = "A characterization of testable hypergraph properties",

abstract = "We provide a combinatorial characterization of all testable properties of k-graphs (i.e. k-uniform hypergraphs). Here, a k-graph property P is testable if there is a randomized algorithm which makes a bounded number of edge queries and distinguishes with probability 2/3 between k-graphs that satisfy P and those that are far from satisfying P. For the 2-graph case, such a combinatorial characterization was obtained by Alon, Fischer, Newman and Shapira. Our results for the k-graph setting are in contrast to those of Austin and Tao, who showed that for the somewhat stronger concept of local repairability, the testability results for graphs do not extend to the 3-graph setting.",

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Joos, F, Kim, J, Kuhn, D & Osthus, D 2017, A characterization of testable hypergraph properties. in Proceedings - 58th Annual IEEE Symposium on Foundations of Computer Science, FOCS 2017. vol. 2017-October, 8104116, IEEE Computer Society Press, pp. 859-867, 58th Annual IEEE Symposium on Foundations of Computer Science, FOCS 2017, Berkeley, United States, 15/10/17. https://doi.org/10.1109/FOCS.2017.84

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N2 - We provide a combinatorial characterization of all testable properties of k-graphs (i.e. k-uniform hypergraphs). Here, a k-graph property P is testable if there is a randomized algorithm which makes a bounded number of edge queries and distinguishes with probability 2/3 between k-graphs that satisfy P and those that are far from satisfying P. For the 2-graph case, such a combinatorial characterization was obtained by Alon, Fischer, Newman and Shapira. Our results for the k-graph setting are in contrast to those of Austin and Tao, who showed that for the somewhat stronger concept of local repairability, the testability results for graphs do not extend to the 3-graph setting.

AB - We provide a combinatorial characterization of all testable properties of k-graphs (i.e. k-uniform hypergraphs). Here, a k-graph property P is testable if there is a randomized algorithm which makes a bounded number of edge queries and distinguishes with probability 2/3 between k-graphs that satisfy P and those that are far from satisfying P. For the 2-graph case, such a combinatorial characterization was obtained by Alon, Fischer, Newman and Shapira. Our results for the k-graph setting are in contrast to those of Austin and Tao, who showed that for the somewhat stronger concept of local repairability, the testability results for graphs do not extend to the 3-graph setting.

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