Searching for protein structure-function relationships using three-dimensional (3D) structural coordinates represents a fundamental approach for determining the function of proteins with unknown functions. Since protein structure databases are rapidly growing in size, the development of a fast search method to find similar protein substructures by comparison of protein 3D structures is essential. In this article, we present a novel protein 3D structure search method to find all substructures

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... h root mean square deviations (RMSDs) to the query structure that are lower than a given threshold value. Our new algorithm runs in O(m + N/m 0.5 ) time, after O(N log N) preprocessing, where N is the database size and m is the query length. The new method is 1.8-41.6 times faster than the practically best known O(N) algorithm, according to computational experiments using a huge database (i.e., > 20,000,000 C-alpha coordinates).