eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2021-06-30
8:1
8:15
10.4230/LIPIcs.CPM.2021.8
article
Weighted Ancestors in Suffix Trees Revisited
Belazzougui, Djamal
1
Kosolobov, Dmitry
2
https://orcid.org/0000-0002-2909-2952
Puglisi, Simon J.
3
https://orcid.org/0000-0001-7668-7636
Raman, Rajeev
4
https://orcid.org/0000-0001-9942-8290
Centre de Recherche sur l'Information Scientifique et Technique, Algiers, Algeria
Institute of Natural Sciences and Mathematics, Ural Federal University, Ekaterinburg, Russia
Department of Computer Science, University of Helsinki, Helsinki, Finland
Department of Informatics, University of Leicester, Leicester, United Kingdom
The weighted ancestor problem is a well-known generalization of the predecessor problem to trees. It is known to require Ω(log log n) time for queries provided 𝒪(n polylog n) space is available and weights are from [0..n], where n is the number of tree nodes. However, when applied to suffix trees, the problem, surprisingly, admits an 𝒪(n)-space solution with constant query time, as was shown by Gawrychowski, Lewenstein, and Nicholson (Proc. ESA 2014). This variant of the problem can be reformulated as follows: given the suffix tree of a string s, we need a data structure that can locate in the tree any substring s[p..q] of s in 𝒪(1) time (as if one descended from the root reading s[p..q] along the way). Unfortunately, the data structure of Gawrychowski et al. has no efficient construction algorithm, limiting its wider usage as an algorithmic tool. In this paper we resolve this issue, describing a data structure for weighted ancestors in suffix trees with constant query time and a linear construction algorithm. Our solution is based on a novel approach using so-called irreducible LCP values.
https://drops.dagstuhl.de/storage/00lipics/lipics-vol191-cpm2021/LIPIcs.CPM.2021.8/LIPIcs.CPM.2021.8.pdf
suffix tree
weighted ancestors
irreducible LCP
deterministic substring hashing