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Partial Recovery of Erdðs-Rényi Graph Alignment via k-Core Alignment

Published:17 December 2019Publication History
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Abstract

We determine information theoretic conditions under which it is possible to partially recover the alignment used to generate a pair of sparse, correlated Erdos-Renyi graphs. To prove our achievability result, we introduce the k-core alignment estimator. This estimator searches for an alignment in which the intersection of the correlated graphs using this alignment has a minimum degree of k. We prove a matching converse bound. As the number of vertices grows, recovery of the alignment for a fraction of the vertices tending to one is possible when the average degree of the intersection of the graph pair tends to infinity. It was previously known that exact alignment is possible when this average degree grows faster than the logarithm of the number of vertices.

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          cover image Proceedings of the ACM on Measurement and Analysis of Computing Systems
          Proceedings of the ACM on Measurement and Analysis of Computing Systems  Volume 3, Issue 3
          SIGMETRICS
          December 2019
          525 pages
          EISSN:2476-1249
          DOI:10.1145/3376928
          Issue’s Table of Contents

          Copyright © 2019 ACM

          Publisher

          Association for Computing Machinery

          New York, NY, United States

          Publication History

          • Published: 17 December 2019
          Published in pomacs Volume 3, Issue 3

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