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Efficient Algorithms for Mining Significant Substructures in Graphs with Quality Guarantees

Graphs have become popular for modeling scientific data in recent years. As a result, techniques for mining graphs are extremely important for understanding inherent data and domain characteristics. One such exploratory mining paradigm is the k-MST (minimum spanning tree over k vertices) problem that can be used to discover significant local substructures. In this paper, we present an efficient approximation algorithm for the k-MST problem in large graphs. The algorithm has an O(radic/k) approximation ratio and O(n log n + in log m log k + nk2 log k) running time, where n and m are the number of vertices and edges respectively. Experimental results on synthetic graphs and protein interaction networks show that the algorithm is scalable to large graphs and useful for discovering biological pathways. The highlight of the algorithm is that it offers both analytical guarantees and empirical evidence of good running time and quality.