Extracting the Sparse Longest Common Prefix Array from the Suffix Binary Search Tree

Abstract

Given a text T of length n, the sparse suffix sorting problem asks for the lexicographic order of suffixes starting at m selectable text positions P. The suffix binary search tree [Irving and Love, JDA’03] is a dynamic data structure that can answer this problem dynamically in the sense that insertions and deletions of positions in P are allowed. While a standard binary search tree on strings needs to store two longest-common prefix (LCP) values per node for providing the same query bounds, each suffix binary search tree node only stores a single LCP value and a bit flag. Its tree topology induces the sorting of the m suffixes by an Euler tour in \({{\mathcal {O}}}(m)\) time. However, it has not been addressed how to compute the lengths of the longest common prefixes of two suffixes with neighboring ranks with this data structure. We show that we can compute these lengths again by an Euler tour in \({{\mathcal {O}}}(m)\) time.