Space Efficient String Mining under Frequency Constraints

Let D₁ and D₂ be two databases (i.e. multisets) of d strings, over an alphabet Sigma, with overall length n. We study the problem of mining discriminative patterns between D₁ and D₂ - e.g., patterns that are frequent in one database but not in the other, emerging patterns, or patterns satisfying other frequency-related constraints. Using the algorithmic framework by Hui (CPM 1992), one can solve several variants of this problem in the optimal linear time with the aid of suffix trees or suffix arrays. This stands in high contrast to other pattern domains such as item-sets or subgraphs, where super-linear lower bounds are known. However, the space requirement of existing solutions is O(n log n) bits, which is not optimal for |Sigma| Lt n (in particular for constant |Sigma|), as the databases themselves occupy only n log |Sigma| bits. Because in many real-life applications space is a more critical resource than time, the aim of this article is to reduce the space, at the cost of an increased running time. In particular, we give a solution for the above problems that uses O(n log |Sigma| + d log n) bits, while the time requirement is increased from the optimal linear time to O(n log n). Our new method is tested extensively on a biologically relevant datasets and shown to be usable even on a genome-scale data.