On the Query Complexity of Testing Orientations for Being Eulerian

Authors:
Eldar Fischer;Oded Lachish;Ilan Newman;Arie Matsliah;Orly Yahalom
Affiliations:
Computer Science Department, Technion - Israel Institute of Technology, Haifa, Israel 32000;Centre for Discrete Mathematics and its Applications (DIMAP), Warwick, UK;Computer Science Department, Haifa University, Haifa, Israel 31905;Computer Science Department, Technion - Israel Institute of Technology, Haifa, Israel 32000;Computer Science Department, Technion - Israel Institute of Technology, Haifa, Israel 32000
Venue:
APPROX '08 / RANDOM '08 Proceedings of the 11th international workshop, APPROX 2008, and 12th international workshop, RANDOM 2008 on Approximation, Randomization and Combinatorial Optimization: Algorithms and Techniques
Year:
2008

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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.