On the query complexity of testing orientations for being Eulerian

Fischer, E. and Lachish, Oded and Newman, I. and Matsliah, A. and Yahalom, O. (2008) On the query complexity of testing orientations for being Eulerian. In: Goel, A. and Jansen, K. and Rolim, J. and Rubinfeld, J. (eds.) Approximation, Randomization and Combinatorial Optimization. Algorithms and Techniques. Lecture Notes in Computer Science 5171. Berlin, Germany: Springer Verlag, pp. 402-415. ISBN 9783540853633.

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Official URL: http://dx.doi.org/10.1007/978-3-540-85363-3_32

Abstract

We consider testing directed graphs for being Eulerian in the orientation model introduced in [15]. Despite the local nature of the property of being Eulerian, it turns out to be significantly harder for testing than other properties studied in the orientation model. We show a non-constant 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 sub-linear 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.

Metadata

Item Type:	Book Section
School:	School of Business, Economics & Informatics > Computer Science and Information Systems
Depositing User:	Sarah Hall
Date Deposited:	30 May 2013 16:05
Last Modified:	11 Oct 2016 12:01
URI:	https://eprints.bbk.ac.uk/id/eprint/7138

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