Seedless Graph Matching via Tail of Degree Distribution for Correlated Erdos-Renyi Graphs
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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 Ω((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 Θ((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 Θ((n)/n) and Θ(^2(n)/n). Experiments show that it outperforms previous works in both regions.
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