Fully-Online Suffix Tree and Directed Acyclic Word Graph Construction for Multiple Texts

Takuya Takagi, Shunsuke Inenaga, Hiroki Arimura, Dany Breslauer, Diptarama Hendrian

Research output: Contribution to journalArticle

Abstract

We consider the construction of the suffix tree and the directed acyclic word graph (DAWG) indexing data structures for a collection T of texts, where a new symbol may be appended to any text in T= { T1, … , TK} , at any time. This fully-online scenario, which arises in dynamically indexing multi-sensor data, is a natural generalization of the long solved semi-online text indexing problem, where texts T1, … , Tk are permanently fixed before the next text Tk + 1 is processed for each k (1 ≤ k< K). We first show that a direct application of Weiner’s right-to-left online construction for the suffix tree of a single text to fully-online multiple texts requires superlinear time. This also means that Blumer et al.’s left-to-right online construction for the DAWG of a single text requires superlinear time in the fully-online setting. We then present our fully-online versions of these algorithms that run in O(Nlog σ) time and O(N) space, where N is the total length of the texts in T and σ is their alphabet size. We then show how to extend Ukkonen’s left-to-right online suffix tree construction to fully-online multiple strings, with the aid of Weiner’s suffix tree for the reversed texts.

Original languageEnglish
JournalAlgorithmica
DOIs
Publication statusAccepted/In press - 2019 Jan 1

Keywords

  • DAWGs
  • Multiple texts
  • Online algorithms
  • String algorithms
  • Suffix trees

ASJC Scopus subject areas

  • Computer Science(all)
  • Computer Science Applications
  • Applied Mathematics

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