Optimal String Mining Under Frequency Constraints

We propose a new algorithmic framework that solves frequency-related data mining queries on databases of strings in optimal time, i.e., in time linear in the input and the output size. The additional space is linear in the input size. Our framework can be used to mine frequent strings, emerging strings and strings that pass other statistical tests, e.g., the χ2-test. In contrast to the presented result for strings, no optimal algorithms are known for other pattern domains such as itemsets. The key to our approach are several recent results on index structures for strings, among them suffix- and lcp-arrays, and a new preprocessing scheme for range minimum queries. The advantages of array-based data structures (compared with dynamic data structures such as trees) are good locality behavior and extensibility to secondary memory. We test our algorithm on real-world data from computational biology and demonstrate that the approach also works well in practice.