Tolerant Bipartiteness Testing in Dense Graphs

Authors Arijit Ghosh, Gopinath Mishra, Rahul Raychaudhury, Sayantan Sen

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Author Details

Arijit Ghosh
  • Indian Statistical Institute, Kolkata, India
Gopinath Mishra
  • University of Warwick, Coventry, UK
Rahul Raychaudhury
  • Duke University, Durham, NC, USA
Sayantan Sen
  • Indian Statistical Institute, Kolkata, India


The authors would like to thank Yufei Zhao, Dingding Dong and Nitya Mani for pointing out a mistake in an earlier version of this paper, as well as the reviewers of ICALP for various suggestions that improved the presentation of the paper.

Cite AsGet BibTex

Arijit Ghosh, Gopinath Mishra, Rahul Raychaudhury, and Sayantan Sen. Tolerant Bipartiteness Testing in Dense Graphs. In 49th International Colloquium on Automata, Languages, and Programming (ICALP 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 229, pp. 69:1-69:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)


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 ε n² entries of the adjacency matrix of G, or we have to edit at least δ n² 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 2^𝒪̃(1/ε) time complexity. This improves upon the state-of-the-art query and time complexities of this problem of 𝒪̃(1/ε⁶) and 2^𝒪̃(1/ε²), respectively, due to Alon, Fernandez de la Vega, Kannan and Karpinski, where 𝒪̃(⋅) hides a factor polynomial in log (1/ε).

Subject Classification

ACM Subject Classification
  • Theory of computation → Streaming, sublinear and near linear time algorithms
  • Tolerant Testing
  • Bipartite Testing
  • Query Complexity
  • Graph Property Testing


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