Order-preserving indexing

Maxime Crochemore, Costas S. Iliopoulos, Tomasz Kociumaka, Marcin Kubica, Alessio Langiu, Solon P. Pissis*, Jakub Radoszewski, Wojciech Rytter, Tomasz Waleń

*Corresponding author for this work

Research output: Contribution to JournalArticleAcademicpeer-review

Abstract

Kubica et al. [33] and Kim et al. [29] introduced order-preserving pattern matching: for a given text the goal is to find its factors having the same 'shape' as a given pattern. Known results include a linear-time algorithm for this problem (in case of polynomially-bounded alphabet) and a generalization to multiple patterns. We propose an index that enables order-preserving pattern matching queries in time proportional to pattern length. The index can be constructed in O(nlog log n) expected time or in O(nlog2 log n/log log log n) worst-case time. It is an incomplete order-preserving suffix tree which may miss a single edge label at each branching node. For most applications such incomplete suffix trees provide the same functional power as the complete ones. We show a number of their applications, including computation of longest common factors, longest previously occurring factors and squares in a string in the order-preserving setting. We also give an O(nlog n)-time algorithm constructing complete order-preserving suffix trees.

Original languageEnglish
Pages (from-to)122-135
Number of pages14
JournalTheoretical Computer Science
Volume638
DOIs
Publication statusPublished - 25 Jul 2016
Externally publishedYes

Keywords

  • Order-preserving indexing
  • Order-preserving matching
  • Suffix tree

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