Seeded graph matching: Efficient algorithms and theoretical guarantees

Farhad Shirani, Siddharth Garg, Elza Erkip

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

In this paper, a new information theoretic framework for graph matching is introduced. Using this framework, the graph isomorphism and seeded graph matching problems are studied. The maximum degree algorithm for graph isomorphism is analyzed and sufficient conditions for successful matching are rederived using type analysis. Furthermore, a new seeded matching algorithm with polynomial time complexity is introduced. The algorithm uses 'typicality matching' and techniques from point-to-point communications for reliable matching. Assuming an Erdös-Renyi model on the correlated graph pair, it is shown that successful matching is guaranteed when the number of seeds grows logarithmically with the number of vertices in the graphs. The logarithmic coefficient is shown to be inversely proportional to the mutual information between the edge variables in the two graphs.

Original languageEnglish (US)
Title of host publicationConference Record of 51st Asilomar Conference on Signals, Systems and Computers, ACSSC 2017
EditorsMichael B. Matthews
PublisherInstitute of Electrical and Electronics Engineers Inc.
Pages253-257
Number of pages5
ISBN (Electronic)9781538618233
DOIs
StatePublished - Apr 10 2018
Event51st Asilomar Conference on Signals, Systems and Computers, ACSSC 2017 - Pacific Grove, United States
Duration: Oct 29 2017Nov 1 2017

Publication series

NameConference Record of 51st Asilomar Conference on Signals, Systems and Computers, ACSSC 2017
Volume2017-October

Other

Other51st Asilomar Conference on Signals, Systems and Computers, ACSSC 2017
CountryUnited States
CityPacific Grove
Period10/29/1711/1/17

ASJC Scopus subject areas

  • Control and Optimization
  • Computer Networks and Communications
  • Hardware and Architecture
  • Signal Processing
  • Biomedical Engineering
  • Instrumentation

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  • Cite this

    Shirani, F., Garg, S., & Erkip, E. (2018). Seeded graph matching: Efficient algorithms and theoretical guarantees. In M. B. Matthews (Ed.), Conference Record of 51st Asilomar Conference on Signals, Systems and Computers, ACSSC 2017 (pp. 253-257). [8335178] (Conference Record of 51st Asilomar Conference on Signals, Systems and Computers, ACSSC 2017; Vol. 2017-October). Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/ACSSC.2017.8335178