Analysis of a Canonical Labeling Algorithm for the Alignment of Correlated Erdos-Rényi Graphs
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 information-theoretic threshold for graph alignment in correlated Erdös-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(n 11/5 log n)-time canonical labeling algorithm, initially introduced in the context of graph isomorphism, succeeds in aligning correlated Erdos-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. Finally, we show that the implementation of a variant of this algorithm allows for the efficient alignment of large graphs under limited noise.
Document Details
- Document Type
- Pub Defense Publication
- Publication Date
- Jun 19, 2019
- Source ID
- 10.1145/3341617.3326151
Entities
People
- Daniel Cullina
- Matthias Grossglauser
- Negar Kiyavash
- Osman Emre Dai
Organizations
- Georgia Tech
- National Science Foundation
- Princeton University
- Swiss Federal Institute of Technology in Lausanne