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.
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Acknowledgments
This work was supported by JSPS KAKENHI Grant Numbers JP21K17701 (DK) and JP19K20213 (TI). We thank the four anonymous reviewers of SPIRE’21 for their valuable comments on our manuscript. They give additional inspiration for Corollary 1 and proposed the problem of how to efficiently merge two suffix binary search tree instances. Tackling this problem could indeed be useful for building and updating FM-indexes and other related indexing data structures.
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I, T., Irving, R.W., Köppl, D., Love, L. (2021). Extracting the Sparse Longest Common Prefix Array from the Suffix Binary Search Tree. In: Lecroq, T., Touzet, H. (eds) String Processing and Information Retrieval. SPIRE 2021. Lecture Notes in Computer Science(), vol 12944. Springer, Cham. https://doi.org/10.1007/978-3-030-86692-1_12
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