Michael Ray, Yves C. Martin
Proceedings of SPIE - The International Society for Optical Engineering
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. © 2012 ACM.
Michael Ray, Yves C. Martin
Proceedings of SPIE - The International Society for Optical Engineering
Richard M. Karp, Raymond E. Miller
Journal of Computer and System Sciences
David W. Jacobs, Daphna Weinshall, et al.
IEEE Transactions on Pattern Analysis and Machine Intelligence
Nimrod Megiddo
Journal of Symbolic Computation