Space-Time Tradeoffs for Longest-Common-Prefix Array Computation

Abstract

The suffix array, a space efficient alternative to the suffix tree, is an important data structure for string processing, enabling efficient and often optimal algorithms for pattern matching, data compression, repeat finding and many problems arising in computational biology. An essential augmentation to the suffix array for many of these tasks is the Longest Common Prefix (LCP) array. In particular the LCP array allows one to simulate bottom-up and top-down traversals of the suffix tree with significantly less memory overhead (but in the same time bounds). Since 2001 the LCP array has been computable in θ(n) time, but the algorithm (even after subsequent refinements) requires relatively large working memory. In this paper we describe a new algorithm that provides a continuous space-time tradeoff for LCP array construction, running in O(nv) time and requiring $n + O(n/\sqrt{v} + v)$ bytes of working space, where v can be chosen to suit the available memory. Furthermore, the algorithm processes the suffix array, and outputs the LCP, strictly left-to-right, making it suitable for use with external memory. We show experimentally that for many naturally occurring strings our algorithm is faster than the linear time algorithms, while using significantly less working memory.