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Partial Recovery in the Graph Alignment Problem

Author

Listed:
  • Georgina Hall

    (Decision Sciences, INSEAD, Fontainebleau 77300, France)

  • Laurent Massoulié

    (DYOGENE, INRIA, Paris 75012, France)

Abstract

In this paper, we consider the graph alignment problem, which is the problem of recovering, given two graphs, a one-to-one mapping between nodes that maximizes edge overlap. This problem can be viewed as a noisy version of the well-known graph isomorphism problem and appears in many applications, including social network deanonymization and cellular biology. Our focus here is on partial recovery ; that is, we look for a one-to-one mapping that is correct on a fraction of the nodes of the graph rather than on all of them, and we assume that the two input graphs to the problem are correlated Erdős–Rényi graphs of parameters ( n , q , s ). Our main contribution is then to give necessary and sufficient conditions on ( n , q , s ) under which partial recovery is possible with high probability as the number of nodes n goes to infinity. In particular, we show that it is possible to achieve partial recovery in the nqs = Θ ( 1 ) regime under certain additional assumptions.

Suggested Citation

  • Georgina Hall & Laurent Massoulié, 2023. "Partial Recovery in the Graph Alignment Problem," Operations Research, INFORMS, vol. 71(1), pages 259-272, January.
    • Handle: RePEc:inm:oropre:v:71:y:2023:i:1:p:259-272
    DOI: 10.1287/opre.2022.2355
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