Efficient LCE Queries and Lexicographic Minimizers on Sliding Suffix Trees

2026-06-30

AI Summary

This work addresses the challenge of efficiently supporting longest common extension (LCE) queries and maintaining the lexicographically smallest suffix in a sliding window suffix tree, where suffixes may reside at implicit nodes as the window slides. To overcome this, the authors introduce a periodic representative mapping that folds implicit suffixes onto explicit leaf nodes. By integrating leaf pointers with a dynamic lowest common ancestor (LCA) structure, they achieve worst-case constant-time LCE queries in an implicit sliding suffix tree for the first time. Additionally, they devise an alternative approach that avoids LCE queries altogether, leveraging a BP-linked suffix tree combined with an order-maintenance structure to update and output the lexicographically smallest suffix in constant time per window slide. The entire framework operates within linear space and supports amortized constant-time window updates over constant-sized alphabets.

Abstract

We study longest-common-extension (LCE) queries and lexicographic minimizer maintenance on the suffix tree of a sliding window. The main difficulty is that a sliding suffix tree is maintained in an implicit Ukkonen-style form: some suffixes of the current window are not represented by leaves. We show that the longest implicit (i.e. non-leaf) suffix induces a periodic representative map that folds every implicit suffix to an explicit suffix leaf in constant time. Combined with leaf pointers [Leonard et al., PSC 2026] and a dynamic LCA data structure [Cole & Hariharan, SICOMP 2005], this yields a linear-space data structure with amortized constant-time window shifts and worst-case constant-time LCE queries over a constant-size alphabet. For minimizers, the LCE structure gives a direct exact solution, but it uses more machinery than fixed-depth comparisons require. We therefore give an alternative LCE-free algorithm that reports minimizers in constant time per window shift, which is built on BP-linked suffix trees [Sumiyoshi et al, SPIRE 2024] and a standard order maintenance data structure (e.g. [Bender et al., ESA 2002]).

Problem

• LCE queries
• lexicographic minimizers
• sliding suffix trees
• implicit suffixes
• sliding window

Innovation

• sliding suffix tree
• longest-common-extension query
• lexicographic minimizers
• implicit suffix folding
• constant-time update