On the Query Complexity of Testing Orientations for Being Eulerian

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 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 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.

• Type: Conference
• Year: 2008
• Where: APPROX
• Authors: Eldar Fischer, Oded Lachish, Ilan Newman, Arie Matsliah, Orly Yahalom
• Keywords: 2-sided Test, Algorithms, APPROX 2008, Orientation Model, Query Complexity