A polynomial‐time approximation scheme for the maximal overlap of two independent Erdős–Rényi graphs
For two independent Erdős–Rényi graphs G(n,p)$$ \mathbf{G}\left(n,p\right) $$, 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 approxi...
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| Veröffentlicht in: | Random structures & algorithms Jg. 65; H. 1; S. 220 - 257 |
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John Wiley & Sons, Inc
01.08.2024
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| Abstract | For two independent Erdős–Rényi graphs G(n,p)$$ \mathbf{G}\left(n,p\right) $$, 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 n2α−1$$ \frac{n}{2\alpha -1} $$ for p=n−α$$ p={n}^{-\alpha } $$ with some constant α∈(1/2,1)$$ \alpha \in \left(1/2,1\right) $$. |
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| AbstractList | For two independent Erdős–Rényi graphs G(n,p)$$ \mathbf{G}\left(n,p\right) $$, 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 n2α−1$$ \frac{n}{2\alpha -1} $$ for p=n−α$$ p={n}^{-\alpha } $$ with some constant α∈(1/2,1)$$ \alpha \in \left(1/2,1\right) $$. For two independent Erdős–Rényi graphs G(n,p)$$ \mathbf{G}\left(n,p\right) $$, 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 n2α−1$$ \frac{n}{2\alpha -1} $$ for p=n−α$$ p={n}^{-\alpha } $$ with some constant α∈(1/2,1)$$ \alpha \in \left(1/2,1\right) $$. 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 . |
| Author | Du, Hang Ding, Jian Gong, Shuyang |
| Author_xml | – sequence: 1 givenname: Jian orcidid: 0000-0002-3078-3793 surname: Ding fullname: Ding, Jian email: dingjian@math.pku.edu.cn organization: Peking University – sequence: 2 givenname: Hang orcidid: 0009-0001-3716-7627 surname: Du fullname: Du, Hang organization: Department of Mathematics, MIT – sequence: 3 givenname: Shuyang orcidid: 0009-0007-2975-4614 surname: Gong fullname: Gong, Shuyang organization: Peking University |
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| Snippet | For two independent Erdős–Rényi graphs G(n,p)$$ \mathbf{G}\left(n,p\right) $$, we study the maximal overlap (i.e., the number of common edges) of these two... 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... For two independent Erdős–Rényi graphs G(n,p)$$ \mathbf{G}\left(n,p\right) $$, we study the maximal overlap (i.e., the number of common edges) of these two... |
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| SubjectTerms | Algorithms Graph theory Graphs greedy algorithm Polynomials polynomial‐time approximation scheme random graph matching |
| Title | A polynomial‐time approximation scheme for the maximal overlap of two independent Erdős–Rényi graphs |
| URI | https://onlinelibrary.wiley.com/doi/abs/10.1002%2Frsa.21212 https://www.proquest.com/docview/3067933181 |
| Volume | 65 |
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