A characterization of testable hypergraph properties
We provide a combinatorial characterization of all testable properties of k-uniform hypergraphs (k-graphs for short). 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 sa...
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| Veröffentlicht in: | Journal of combinatorial theory. Series B Jg. 174; S. 133 - 189 |
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| Abstract | We provide a combinatorial characterization of all testable properties of k-uniform hypergraphs (k-graphs for short). 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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| AbstractList | We provide a combinatorial characterization of all testable properties of k-uniform hypergraphs (k-graphs for short). 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. |
| Author | Joos, Felix Kühn, Daniela Kim, Jaehoon Osthus, Deryk |
| Author_xml | – sequence: 1 givenname: Felix orcidid: 0000-0002-8539-9641 surname: Joos fullname: Joos, Felix email: joos@informatik.uni-heidelberg.de organization: Institut für Informatik, Universität Heidelberg, Germany – sequence: 2 givenname: Jaehoon surname: Kim fullname: Kim, Jaehoon email: jaehoon.kim@kaist.ac.kr organization: Department of Mathematical Sciences, KAIST, 34141, South Korea – sequence: 3 givenname: Daniela surname: Kühn fullname: Kühn, Daniela email: d.kuhn@bham.ac.uk organization: School of Mathematics, University of Birmingham, Edgbaston, Birmingham, B15 2TT, United Kingdom – sequence: 4 givenname: Deryk surname: Osthus fullname: Osthus, Deryk email: d.osthus@bham.ac.uk organization: School of Mathematics, University of Birmingham, Edgbaston, Birmingham, B15 2TT, United Kingdom |
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| Keywords | Hypergraphs Sublinear algorithms Property testing |
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| Snippet | We provide a combinatorial characterization of all testable properties of k-uniform hypergraphs (k-graphs for short). Here, a k-graph property P is testable if... |
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| SubjectTerms | Hypergraphs Property testing Sublinear algorithms |
| Title | A characterization of testable hypergraph properties |
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