An invertible transform for efficient string matching in Labeled Digraphs

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

2 Scopus citations

Abstract

Let G = (V,E) be a digraph where each vertex is unlabeled, each edge is labeled by a character in some alphabet O, and any two edges with both the same head and the same tail have different labels. The powerset construction gives a transform of G into a weakly connected digraph G' = (V ',E') that enables solving the decision problem of whether there is a walk in G matching an arbitrarily long query string q in time linear in |q| and independent of |E| and |V |. We show G is uniquely determined by G' when for every vl ϵ V, there is some distinct string sl on O such that vl is the origin of a closed walk in G matching sl, and no other walk in G matches sl unless it starts and ends at vl. We then exploit this invertibility condition to strategically alter any G so its transform G' enables retrieval of all t terminal vertices of walks in the unaltered G matching q in O(|q| + t log |V |) time. We conclude by proposing two defining properties of a class of transforms that includes the Burrows-Wheeler transform and the transform presented here.

Original languageEnglish (US)
Title of host publication32nd Annual Symposium on Combinatorial Pattern Matching, CPM 2021
EditorsPawel Gawrychowski, Tatiana Starikovskaya
PublisherSchloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing
ISBN (Electronic)9783959771863
DOIs
StatePublished - Jul 1 2021
Event32nd Annual Symposium on Combinatorial Pattern Matching, CPM 2021 - Wroclaw, Poland
Duration: Jul 5 2021Jul 7 2021

Publication series

NameLeibniz International Proceedings in Informatics, LIPIcs
Volume191
ISSN (Print)1868-8969

Conference

Conference32nd Annual Symposium on Combinatorial Pattern Matching, CPM 2021
Country/TerritoryPoland
CityWroclaw
Period7/5/217/7/21

Keywords

  • Burrows-Wheeler transform
  • Labeled graphs
  • Pattern matching
  • String matching

ASJC Scopus subject areas

  • Software

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