Analysis of a canonical labeling algorithm for the alignment of correlated Erdos-Rényi graphs

Osman Emre Dai, Daniel Cullina, Negar Kiyavash, Matthias Grossglauser

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

Abstract

Graph alignment in two correlated random graphs refers to the task of identifying the correspondence between vertex sets of the graphs. Recent results have characterized the exact informationtheoretic threshold for graph alignment in correlated Erdos-Rényi graphs. However, very little is known about the existence of efficient algorithms to achieve graph alignment without seeds. In this work we identify a region in which a straightforward O(n11/5 logn)-time canonical labeling algorithm, initially introduced in the context of graph isomorphism, succeeds in aligning correlated Erd?s-Rényi graphs. The algorithm has two steps. In the first step, all vertices are labeled by their degrees and a trivial minimum distance alignment (i.e., sorting vertices according to their degrees) matches a fixed number of highest degree vertices in the two graphs. Having identified this subset of vertices, the remaining vertices are matched using a alignment algorithm for bipartite graphs.

Original languageEnglish (US)
Title of host publicationSIGMETRICS Performance 2019 - Abstracts of the 2019 SIGMETRICS/Performance Joint International Conference on Measurement and Modeling of Computer Systems
PublisherAssociation for Computing Machinery, Inc
Pages97-98
Number of pages2
ISBN (Electronic)9781450366786
DOIs
StatePublished - Jun 20 2019
Event14th Joint Conference of International Conference on Measurement and Modeling of Computer Systems, SIGMETRICS 2019 and IFIP Performance Conference 2019, SIGMETRICS/Performance 2019 - Phoenix, United States
Duration: Jun 24 2019Jun 28 2019

Publication series

NameSIGMETRICS Performance 2019 - Abstracts of the 2019 SIGMETRICS/Performance Joint International Conference on Measurement and Modeling of Computer Systems

Conference

Conference14th Joint Conference of International Conference on Measurement and Modeling of Computer Systems, SIGMETRICS 2019 and IFIP Performance Conference 2019, SIGMETRICS/Performance 2019
CountryUnited States
CityPhoenix
Period6/24/196/28/19

All Science Journal Classification (ASJC) codes

  • Hardware and Architecture
  • Computer Networks and Communications
  • Computational Theory and Mathematics

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  • Cite this

    Dai, O. E., Cullina, D., Kiyavash, N., & Grossglauser, M. (2019). Analysis of a canonical labeling algorithm for the alignment of correlated Erdos-Rényi graphs. In SIGMETRICS Performance 2019 - Abstracts of the 2019 SIGMETRICS/Performance Joint International Conference on Measurement and Modeling of Computer Systems (pp. 97-98). (SIGMETRICS Performance 2019 - Abstracts of the 2019 SIGMETRICS/Performance Joint International Conference on Measurement and Modeling of Computer Systems). Association for Computing Machinery, Inc. https://doi.org/10.1145/3309697.3331505