TY - JOUR
T1 - Improved Achievability and Converse Bounds for Erdos-Renyi Graph Matching
AU - Cullina, Daniel
AU - Kiyavash, Negar
N1 - Funding Information:
This work was in part supported by supported by MURI grant ARMY W911NF-15-1-0479 and NSF grant CCF 10-54937 - CAREER.
Publisher Copyright:
© 2016 ACM.
PY - 2016/6
Y1 - 2016/6
N2 - We consider the problem of perfectly recovering the vertex correspondence between two correlated Erdos-Renyi (ER) graphs. For a pair of correlated graphs on the same vertex set, the correspondence between the vertices can be obscured by randomly permuting the vertex labels of one of the graphs. In some cases, the structural information in the graphs allow this correspondence to be recovered. We investigate the information-theoretic threshold for exact recovery, i.e. the conditions under which the entire vertex correspondence can be correctly recovered given unbounded computational resources. Pedarsani and Grossglauser provided an achievability result of this type. Their result establishes the scaling dependence of the threshold on the number of vertices. We improve on their achievability bound. We also provide a converse bound, establishing conditions under which exact recovery is impossible. Together, these establish the scaling dependence of the threshold on the level of correlation between the two graphs. The converse and achievability bounds differ by a factor of two for sparse, significantly correlated graphs.
AB - We consider the problem of perfectly recovering the vertex correspondence between two correlated Erdos-Renyi (ER) graphs. For a pair of correlated graphs on the same vertex set, the correspondence between the vertices can be obscured by randomly permuting the vertex labels of one of the graphs. In some cases, the structural information in the graphs allow this correspondence to be recovered. We investigate the information-theoretic threshold for exact recovery, i.e. the conditions under which the entire vertex correspondence can be correctly recovered given unbounded computational resources. Pedarsani and Grossglauser provided an achievability result of this type. Their result establishes the scaling dependence of the threshold on the number of vertices. We improve on their achievability bound. We also provide a converse bound, establishing conditions under which exact recovery is impossible. Together, these establish the scaling dependence of the threshold on the level of correlation between the two graphs. The converse and achievability bounds differ by a factor of two for sparse, significantly correlated graphs.
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U2 - 10.1145/2896377.2901460
DO - 10.1145/2896377.2901460
M3 - Article
AN - SCOPUS:85112743853
VL - 44
SP - 63
EP - 72
JO - Performance Evaluation Review
JF - Performance Evaluation Review
SN - 0163-5999
IS - 1
ER -