Seedless Graph Matching via Tail of Degree Distribution for Correlated Erdos-Renyi Graphs
The graph matching problem refers to recovering the node-to-node correspondence between two correlated graphs. A previous work theoretically showed that recovering is feasible in sparse Erdos-Renyi graphs if and only if the probability of having an edge between a pair of nodes in one of the graphs and also between the corresponding nodes in the other graph is in the order of $\Omega(\log(n)/n)$, where n is the number of nodes. In this paper, we propose a graph matching algorithm which obtains correct matching with high probability in Erdos-Renyi graphs for the region of $\Theta(\log(n)/n)$ without using a seed set of pre-matched node pairs as an input. The algorithm assigns structurally innovative features to high-degree nodes based on the tail of empirical degree distribution of their neighbor nodes. Then, it matches the high-degree nodes according to these features, and finally obtains a matching for the remaining nodes. We evaluate the performance of proposed algorithm in the regions of $\Theta(\log(n)/n)$ and $\Theta(\log^{2}(n)/n)$. Experiments show that it outperforms previous works in both regions.