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...

Celý popis

Uložené v:

Podrobná bibliografia
Vydané v:	Random structures & algorithms Ročník 65; číslo 1; s. 220 - 257
Hlavní autori:	Ding, Jian, Du, Hang, Gong, Shuyang
Médium:	Journal Article
Jazyk:	English
Vydavateľské údaje:	New York John Wiley & Sons, Inc 01.08.2024 Wiley Subscription Services, Inc
Predmet:	Algorithms Graph theory Graphs greedy algorithm Polynomials polynomial‐time approximation scheme random graph matching
ISSN:	1042-9832, 1098-2418
On-line prístup:	Získať plný text
Tagy:	Pridať tag Žiadne tagy, Buďte prvý, kto otaguje tento záznam!

Popis
Shrnutí:	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)$$ \alpha \in \left(1/2,1\right) $$.
Bibliografia:	ObjectType-Article-1 SourceType-Scholarly Journals-1 ObjectType-Feature-2 content type line 14
ISSN:	1042-9832 1098-2418
DOI:	10.1002/rsa.21212