Matching Graphs with Community Structure: A Concentration of Measure Approach

Farhad Shirani, Siddharth Garg, Elza Erkip

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

Abstract

In this paper, matching pairs of random graphs under the community structure model is considered. The problem emerges naturally in various applications such as privacy, image processing and DNA sequencing. A pair of randomly generated labeled graphs with pairwise correlated edges are considered. It is assumed that the graph edges are generated based on the community structure model. Given the labeling of the edges of the first graph, the objective is to recover the labels in the second graph. The problem is considered under two scenarios: i) with side-information where the community membership of the nodes in both graphs are known, and ii) without side-information where the community memberships are not known. A matching scheme is proposed which operates based on typicality of the adjacency matrices of the graphs. Achievability results are derived which provide theoretical guarantees for successful matching under specific assumptions on graph parameters. It is observed that for the proposed matching scheme, the conditions for successful matching do not change in the presence of side-information. Furthermore, a converse result is derived which characterizes a set of graph parameters for which matching is not possible.

Original languageEnglish (US)
Title of host publication2018 56th Annual Allerton Conference on Communication, Control, and Computing, Allerton 2018
PublisherInstitute of Electrical and Electronics Engineers Inc.
Pages1028-1035
Number of pages8
ISBN (Electronic)9781538665961
DOIs
StatePublished - Feb 5 2019
Event56th Annual Allerton Conference on Communication, Control, and Computing, Allerton 2018 - Monticello, United States
Duration: Oct 2 2018Oct 5 2018

Publication series

Name2018 56th Annual Allerton Conference on Communication, Control, and Computing, Allerton 2018

Conference

Conference56th Annual Allerton Conference on Communication, Control, and Computing, Allerton 2018
CountryUnited States
CityMonticello
Period10/2/1810/5/18

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ASJC Scopus subject areas

  • Computer Networks and Communications
  • Hardware and Architecture
  • Signal Processing
  • Energy Engineering and Power Technology
  • Control and Optimization

Cite this

Shirani, F., Garg, S., & Erkip, E. (2019). Matching Graphs with Community Structure: A Concentration of Measure Approach. In 2018 56th Annual Allerton Conference on Communication, Control, and Computing, Allerton 2018 (pp. 1028-1035). [8636015] (2018 56th Annual Allerton Conference on Communication, Control, and Computing, Allerton 2018). Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/ALLERTON.2018.8636015