Theoretical study reveals a polynomial-time approximation scheme for maximal overlap in independent Erdős–Rényi graphs, indicating efficient bounds for random graph matching.
For two independent Erdős–Rényi graphs , we study the maximal overlap (i.e., the number of common edges) of these two graphs over all possible vertex correspondence. We present a polynomial‐time algorithm which finds a vertex correspondence whose overlap approximates the maximal overlap up to a multiplicative factor that is arbitrarily close to 1. As a by‐product, we prove that the maximal overlap is asymptotically for with some constant .
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Ding et al. (2024) studied this question.
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