TY - CHAP
T1 - Tight bounds for testing bipartiteness in general graphs
AU - Kaufman, Tali
AU - Krivelevich, Michael
AU - Ron, Dana
PY - 2003
Y1 - 2003
N2 - 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.
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.
UR - http://www.scopus.com/inward/record.url?scp=26944436398&partnerID=8YFLogxK
U2 - 10.1007/978-3-540-45198-3_29
DO - 10.1007/978-3-540-45198-3_29
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AN - SCOPUS:26944436398
SN - 3540407707
SN - 9783540407706
T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
SP - 341
EP - 353
BT - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
A2 - Asora, Sanjeev
A2 - Sahai, Amit
A2 - Jansen, Klaus
A2 - Rolim, Jose D.P.
PB - Springer Verlag
ER -