Tolerant Bipartiteness Testing in Dense Graphs

Document Type

Conference Article

Publication Title

Leibniz International Proceedings in Informatics, LIPIcs


Bipartite testing has been a central problem in the area of property testing since its inception in the seminal work of Goldreich, Goldwasser, and Ron. Though the non-tolerant version of bipartite testing has been extensively studied in the literature, the tolerant variant is not well understood. In this paper, we consider the following version of tolerant bipartite testing problem: Given two parameters ε, δ ∈ (0, 1), with δ > ε, and access to the adjacency matrix of a graph G, we have to decide whether G can be made bipartite by editing at most εn2 entries of the adjacency matrix of G, or we have to edit at least δn2 entries of the adjacency matrix to make G bipartite. In this paper, we prove that for δ = (2 + Ω(1))ε, tolerant bipartite testing can be decided by performing Õ (1/ε3) many adjacency queries and in 2Oe(1/ε) time complexity. This improves upon the state-of-the-art query and time complexities of this problem of Õ (1/ε6) and 2Oe(1/ε2), respectively, due to Alon, Fernandez de la Vega, Kannan and Karpinski, where Oe(·) hides a factor polynomial in log (1/ε).



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