Suffix Trees, DAWGs and CDAWGs for Forward and Backward Tries

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

The suffix tree, DAWG, and CDAWG are fundamental indexing structures of a string, with a number of applications in bioinformatics, information retrieval, data mining, etc. An edge-labeled rooted tree (trie) is a natural generalization of a string, which can also be seen as a compact representation of a set of strings. Kosaraju [FOCS 1989] proposed the suffix tree for a backward trie, where the strings in the trie are read in the leaf-to-root direction. In contrast to a backward trie, we call a usual trie as a forward trie. Despite a few follow-up works after Kosaraju’s paper, indexing forward/backward tries is not well understood yet. In this paper, we show a full perspective on the sizes of indexing structures such as suffix trees, DAWGs, and CDAWGs for forward and backward tries. In particular, we show that the size of the DAWG for a forward trie with n nodes is Ω(σn), where σ is the number of distinct characters in the trie. This becomes Ω(n2) for an alphabet of size σ= Θ(n). Still, we show that there is a compact O(n)-space implicit representation of the DAWG for a forward trie, whose space requirement is independent of the alphabet size. This compact representation allows for simulating each DAWG edge traversal in O(log σ) time, and can be constructed in O(n) time and space over any integer alphabet of size O(n).

Original languageEnglish
Title of host publicationLATIN 2020
Subtitle of host publicationTheoretical Informatics - 14th Latin American Symposium 2021, Proceedings
EditorsYoshiharu Kohayakawa, Flávio Keidi Miyazawa
PublisherSpringer Science and Business Media Deutschland GmbH
Pages194-206
Number of pages13
ISBN (Print)9783030617912
DOIs
Publication statusPublished - 2020
Event14th Latin American Symposium on Theoretical Informatics, LATIN 2020 - Sao Paulo, Brazil
Duration: Jan 5 2021Jan 8 2021

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume12118 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Conference

Conference14th Latin American Symposium on Theoretical Informatics, LATIN 2020
CountryBrazil
CitySao Paulo
Period1/5/211/8/21

All Science Journal Classification (ASJC) codes

  • Theoretical Computer Science
  • Computer Science(all)

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