Seeded graph matching via large neighborhood statistics
Name
1807.10262.pdf
Description
Submitted version
Size
396.05 KB
Format
Adobe PDF
Checksum (MD5)
b1ed0dbd80f9c68771f0171c1d2bda92
Author(s)
Mossel, E
Xu, J
Date Issued
October 1, 2020
Journal
Random Structures and Algorithms
Publisher
Wiley
Version
Original manuscript
Abstract
© 2020 Wiley Periodicals, LLC. 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 vertices n. Moreover, we show the number of seeds needed for perfect recovery in polynomial-time can be as low as (Formula presented.) in the sparse graph regime (with the average degree smaller than (Formula presented.)) and (Formula presented.) in the dense graph regime, for a small positive constant (Formula presented.). 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.
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
Terms of Use
Creative Commons Attribution-Noncommercial-Share Alike
Persistent DSpace Link
DOI of Published Version
https://doi.org/10.1002/rsa.20934
