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Title: Seeded graph matching via large neighborhood statistics

We study a noisy graph isomorphism problem, where the goal is to perfectly recover the vertex correspondence between two edge‐correlated graphs, with an initial seed set of correctly matched vertex pairs revealed as side information. We show that it is possible to achieve the information‐theoretic limit of graph sparsity in time polynomial in the number of verticesn. Moreover, we show the number of seeds needed for perfect recovery in polynomial‐time can be as low asin the sparse graph regime (with the average degree smaller than) andin the dense graph regime, for a small positive constant. Unlike previous work on graph matching, which used small neighborhoods or small subgraphs with a logarithmic number of vertices in order to match vertices, our algorithms match vertices if their large neighborhoods have a significant overlap in the number of seeds.

 
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Award ID(s):
1850743 1932630 1856424
NSF-PAR ID:
10166755
Author(s) / Creator(s):
 ;  
Publisher / Repository:
Wiley Blackwell (John Wiley & Sons)
Date Published:
Journal Name:
Random Structures & Algorithms
Volume:
57
Issue:
3
ISSN:
1042-9832
Page Range / eLocation ID:
p. 570-611
Format(s):
Medium: X
Sponsoring Org:
National Science Foundation
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