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Graph Reconstruction with a Connected Components Oracle

Authors Juha Harviainen , Pekka Parviainen

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Subject Classification

ACM Subject Classification
  • Theory of computation → Graph algorithms analysis
Keywords
  • graph reconstruction
  • parameterized complexity
  • query complexity

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Abstract

In the Graph Reconstruction (GR) problem, the goal is to recover a hidden graph by utilizing some oracle that provides limited access to the structure of the graph. The interest is in characterizing how strong different oracles are when the complexity of an algorithm is measured in the number of performed queries. We study a novel oracle that returns the set of connected components (CC) on the subgraph induced by the queried subset of vertices. Our main contributions are as follows:  
1) For a hidden graph with n vertices, m edges, maximum degree Δ, and treewidth k, GR can be solved in 𝒪(min{m/log m, Δ², k²} ⋅ log n) CC queries by an adaptive randomized algorithm. 
2) For a hidden graph with n vertices and degeneracy d, GR can be solved in 𝒪(d² log² n) CC queries by an adaptive randomized algorithm. 
3) There are hidden graphs with n vertices, m edges, maximum degree Δ, treewidth k, and degeneracy d such that Ω(m), Ω(Δ²), Ω(k²), and Ω(d²) CC queries are required for solving GR.

Cite As Get BibTex

Juha Harviainen and Pekka Parviainen. Graph Reconstruction with a Connected Components Oracle. In 52nd International Workshop on Graph-Theoretic Concepts in Computer Science (WG 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 376, pp. 24:1-24:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026) https://doi.org/10.4230/LIPIcs.WG.2026.24

Author Details

Juha Harviainen
  • Department of Computer Science, University of Helsinki, Finland
Pekka Parviainen
  • Department of Informatics, University of Bergen, Norway

Funding

  • Harviainen, Juha: Co-funded by the Research Council of Finland, Grant 351156. Co-funded by the European Union (ERC, SCALEBIO, 101169716). Views and opinions expressed are however those of the author(s) only and do not necessarily reflect those of the European Union or the European Research Council. Neither the European Union nor the granting authority can be held responsible for them.
  • Parviainen, Pekka: This work was supported by L. Meltzers Høyskolefond.

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