On the query complexity of testing orientations for being Eulerian

Authors:
Eldar Fischer;Oded Lachish;Arie Matsliah;Ilan Newman;Orly Yahalom
Affiliations:
Technion, Israel Institute of Technology;Birkbeck, University of London;IBM Research and Technion, Israel Institute of Technology;University of Haifa;ORT Braude College, Israel
Venue:
ACM Transactions on Algorithms (TALG)
Year:
2012

Citing 14
Cited 1

Self-testing/correcting with applications to numerical problems

Journal of Computer and System Sciences - Special issue: papers from the 22nd ACM symposium on the theory of computing, May 14–16, 1990
Property testing and its connection to learning and approximation

Journal of the ACM (JACM)
Robust Characterizations of Polynomials withApplications to Program Testing

SIAM Journal on Computing
Testing Membership in Languages that Have Small Width Branching Programs

SIAM Journal on Computing
Testing the diameter of graphs

Random Structures & Algorithms
Testing properties of directed graphs: acyclicity and connectivity

Random Structures & Algorithms
Tight Bounds for Testing Bipartiteness in General Graphs

SIAM Journal on Computing
Testing subgraphs in directed graphs

Journal of Computer and System Sciences - Special issue: STOC 2003
Some 3CNF Properties Are Hard to Test

SIAM Journal on Computing
On the diameter of Eulerian orientations of graphs

SODA '06 Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm
Testing Properties of Constraint-Graphs

CCC '07 Proceedings of the Twenty-Second Annual IEEE Conference on Computational Complexity
Probabilistic computations: Toward a unified measure of complexity

SFCS '77 Proceedings of the 18th Annual Symposium on Foundations of Computer Science
Testing st-Connectivity

APPROX '07/RANDOM '07 Proceedings of the 10th International Workshop on Approximation and the 11th International Workshop on Randomization, and Combinatorial Optimization. Algorithms and Techniques
Testing Convexity Properties of Tree Colorings

Algorithmica

Testing formula satisfaction

SWAT'12 Proceedings of the 13th Scandinavian conference on Algorithm Theory

Quantified Score

Hi-index	0.00

Visualization

Abstract

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.