Tight bounds for testing bipartiteness in general graphs

Tali Kaufman; Michael Krivelevich; Dana Ron

doi:10.1007/978-3-540-45198-3_29

Tight bounds for testing bipartiteness in general graphs

Tali Kaufman^*, Michael Krivelevich, Dana Ron

^*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

Abstract

In this paper we consider the problem of testing bipartiteness of general graphs. The problem has previously been studied in two models, one most suitable for dense graphs, and one most suitable for bounded-degree graphs. Roughly speaking, dense graphs can be tested for bipartiteness with constant complexity, while the complexity of testing bounded-degree graphs is θ̃(√n), where n is the number of vertices in the graph. Thus there is a large gap between the complexity of testing in the two cases. In this work we bridge the gap described above. In particular, we study the problem of testing bipartiteness in a model that is suitable for all densities. We present an algorithm whose complexity is Õ(min(√n,n²/m)) where m is the number of edges in the graph, and match it with an almost tight lower bound.

Original language	English
Title of host publication	Approximation, Randomization, and Combinatorial Optimization : Algorithms and Techniques
Subtitle of host publication	6th International Workshop on Approximation Algorithms for Combinatorial Optimization Problems, APPROX 2003 and 7th International Workshop on Randomization and Approximation Techniques in Computer Science, RANDOM 2003, Princeton, NJ, USA, August 24-26, 2003. Proceedings
Editors	Sanjeev Asora, Klaus Jansen, Jose D.P. Rolim, Amit Sahai
Place of Publication	Berlin Heidelberg
Publisher	Springer Verlag
Pages	341-353
Number of pages	13
ISBN (Electronic)	978-3-540-45198-3
ISBN (Print)	3540407707, 9783540407706
DOIs	https://doi.org/10.1007/978-3-540-45198-3_29
State	Published - 2003

Publication series

Name	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume	2764
ISSN (Print)	0302-9743
ISSN (Electronic)	1611-3349

Keywords

Average degree
Regular graph
query complexity
testing algorithm

Access to Document

10.1007/978-3-540-45198-3_29

Cite this

Kaufman, T., Krivelevich, M., & Ron, D. (2003). Tight bounds for testing bipartiteness in general graphs. In S. Asora, K. Jansen, J. D. P. Rolim, & A. Sahai (Eds.), Approximation, Randomization, and Combinatorial Optimization : Algorithms and Techniques: 6th International Workshop on Approximation Algorithms for Combinatorial Optimization Problems, APPROX 2003 and 7th International Workshop on Randomization and Approximation Techniques in Computer Science, RANDOM 2003, Princeton, NJ, USA, August 24-26, 2003. Proceedings (pp. 341-353). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 2764). Springer Verlag. https://doi.org/10.1007/978-3-540-45198-3_29

Kaufman, Tali ; Krivelevich, Michael ; Ron, Dana. / Tight bounds for testing bipartiteness in general graphs. Approximation, Randomization, and Combinatorial Optimization : Algorithms and Techniques: 6th International Workshop on Approximation Algorithms for Combinatorial Optimization Problems, APPROX 2003 and 7th International Workshop on Randomization and Approximation Techniques in Computer Science, RANDOM 2003, Princeton, NJ, USA, August 24-26, 2003. Proceedings. editor / Sanjeev Asora ; Klaus Jansen ; Jose D.P. Rolim ; Amit Sahai. Berlin Heidelberg : Springer Verlag, 2003. pp. 341-353 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).

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Kaufman, T, Krivelevich, M & Ron, D 2003, Tight bounds for testing bipartiteness in general graphs. in S Asora, K Jansen, JDP Rolim & A Sahai (eds), Approximation, Randomization, and Combinatorial Optimization : Algorithms and Techniques: 6th International Workshop on Approximation Algorithms for Combinatorial Optimization Problems, APPROX 2003 and 7th International Workshop on Randomization and Approximation Techniques in Computer Science, RANDOM 2003, Princeton, NJ, USA, August 24-26, 2003. Proceedings. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 2764, Springer Verlag, Berlin Heidelberg, pp. 341-353. https://doi.org/10.1007/978-3-540-45198-3_29

Tight bounds for testing bipartiteness in general graphs. / Kaufman, Tali; Krivelevich, Michael ; Ron, Dana.
Approximation, Randomization, and Combinatorial Optimization : Algorithms and Techniques: 6th International Workshop on Approximation Algorithms for Combinatorial Optimization Problems, APPROX 2003 and 7th International Workshop on Randomization and Approximation Techniques in Computer Science, RANDOM 2003, Princeton, NJ, USA, August 24-26, 2003. Proceedings. ed. / Sanjeev Asora; Klaus Jansen; Jose D.P. Rolim; Amit Sahai. Berlin Heidelberg: Springer Verlag, 2003. p. 341-353 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 2764).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

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AB - In this paper we consider the problem of testing bipartiteness of general graphs. The problem has previously been studied in two models, one most suitable for dense graphs, and one most suitable for bounded-degree graphs. Roughly speaking, dense graphs can be tested for bipartiteness with constant complexity, while the complexity of testing bounded-degree graphs is θ̃(√n), where n is the number of vertices in the graph. Thus there is a large gap between the complexity of testing in the two cases. In this work we bridge the gap described above. In particular, we study the problem of testing bipartiteness in a model that is suitable for all densities. We present an algorithm whose complexity is Õ(min(√n,n2/m)) where m is the number of edges in the graph, and match it with an almost tight lower bound.

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Kaufman T, Krivelevich M , Ron D. Tight bounds for testing bipartiteness in general graphs. In Asora S, Jansen K, Rolim JDP, Sahai A, editors, Approximation, Randomization, and Combinatorial Optimization : Algorithms and Techniques: 6th International Workshop on Approximation Algorithms for Combinatorial Optimization Problems, APPROX 2003 and 7th International Workshop on Randomization and Approximation Techniques in Computer Science, RANDOM 2003, Princeton, NJ, USA, August 24-26, 2003. Proceedings. Berlin Heidelberg: Springer Verlag. 2003. p. 341-353. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). doi: 10.1007/978-3-540-45198-3_29

Tight bounds for testing bipartiteness in general graphs

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