Arnon Amir, Michael Lindenbaum
IEEE Transactions on Pattern Analysis and Machine Intelligence
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.
Arnon Amir, Michael Lindenbaum
IEEE Transactions on Pattern Analysis and Machine Intelligence
Richard M. Karp, Raymond E. Miller
Journal of Computer and System Sciences
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Ergodic Theory and Dynamical Systems
Minghong Fang, Zifan Zhang, et al.
CCS 2024