TY - GEN
T1 - Analysis of a canonical labeling algorithm for the alignment of correlated Erdos-Rényi graphs
AU - Dai, Osman Emre
AU - Cullina, Daniel
AU - Kiyavash, Negar
AU - Grossglauser, Matthias
PY - 2019/6/20
Y1 - 2019/6/20
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=85069147139&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=85069147139&partnerID=8YFLogxK
U2 - 10.1145/3309697.3331505
DO - 10.1145/3309697.3331505
M3 - Conference contribution
T3 - SIGMETRICS Performance 2019 - Abstracts of the 2019 SIGMETRICS/Performance Joint International Conference on Measurement and Modeling of Computer Systems
SP - 97
EP - 98
BT - SIGMETRICS Performance 2019 - Abstracts of the 2019 SIGMETRICS/Performance Joint International Conference on Measurement and Modeling of Computer Systems
PB - Association for Computing Machinery, Inc
T2 - 14th Joint Conference of International Conference on Measurement and Modeling of Computer Systems, SIGMETRICS 2019 and IFIP Performance Conference 2019, SIGMETRICS/Performance 2019
Y2 - 24 June 2019 through 28 June 2019
ER -