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    On the query complexity of testing orientations for being Eulerian

    Fischer, E. and Lachish, Oded and Matsliah, A. and Newman, I. and Yahalom, O. (2012) On the query complexity of testing orientations for being Eulerian. ACM Transactions on Algorithms 8 (2), pp. 1-41. ISSN 1549-6325.

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    We consider testing directed graphs Eulerianity in the orientation model introduced in Halevy et al. [2005]. Despite the local nature of the Eulerian property, it turns out to be significantly harder to test than other properties studied in the orientation model. We show a nonconstant lower bound on the query complexity of 2-sided tests and a linear lower bound on the query complexity of 1-sided tests for this property. On the positive side, we give several 1-sided and 2-sided tests, including a sublinear query complexity 2-sided test, for general graphs. For special classes of graphs, including bounded-degree graphs and expander graphs, we provide improved results. In particular, we give a 2-sided test with constant query complexity for dense graphs, as well as for expander graphs with a constant expansion parameter.


    Item Type: Article
    School: Birkbeck Faculties and Schools > Faculty of Science > School of Computing and Mathematical Sciences
    Depositing User: Sarah Hall
    Date Deposited: 30 May 2013 13:12
    Last Modified: 09 Aug 2023 12:33


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