Efficiency of fast parallel pattern searching in highly compressed texts

Leszek Gąsieniec, Alan Gibbons, Wojciech Rytter

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

5 Scopus citations

Abstract

We consider efficiency of NC-algorithms for pattern-searching in highly compressed one- and two-dimensional texts. “Highly compressed” means that the text can be exponentially large with respect to its compressed version, and “fast” means “in polylogarithmic time”. Given an uncompressed pattern P and a compressed version of a text T, the compressed matching problem is to test if P occurs in T. Two types of closely related compressed representations of 1-dimensional texts are considered: the Lempel-Ziv encodings (LZ, in short) and restricted LZ encodings (RLZ, in short). For highly compressed texts there is a small difference between them, in extreme situations both of them compress text exponentially, e.g. Fibonacci words of size N have compressed versions of size O(logN) for LZ and Restricted LZ encodings. Despite similarities we prove that LZ-compressed matching is P-complete while RLZ-compressed matching is rather trivially in NC. We show how to improve a naive straightforward NC algorithm and obtain almost optimal parallel RLZ-compressed matching applying tree-contraction techniques to directed acyclic graphs with polynomial tree-size. As a corollary we obtain an almost optimal parallel algorithm for LZW-compressed matching which is simpler than the (more general) algorithm in [11]. Highly compressed 2-dimensional texts are also considered.

Original languageEnglish (US)
Title of host publicationMathematical Foundations of Computer Science 1999 - 24th International Symposium, MFCS 1999, Proceedings
EditorsMirosław kutyłowski, Leszek Pacholski, Tomasz Wierzbicki
PublisherSpringer Verlag
Pages48-58
Number of pages11
ISBN (Print)3540664084, 9783540664086
DOIs
StatePublished - Jan 1 1999
Externally publishedYes
Event24th International Symposium on Mathematical Foundations of Computer Science, MFCS 1999 - Szklarska Poreba, Poland
Duration: Sep 6 1999Sep 10 1999

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume1672
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Conference

Conference24th International Symposium on Mathematical Foundations of Computer Science, MFCS 1999
CountryPoland
CitySzklarska Poreba
Period9/6/999/10/99

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computer Science(all)

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  • Cite this

    Gąsieniec, L., Gibbons, A., & Rytter, W. (1999). Efficiency of fast parallel pattern searching in highly compressed texts. In M. kutyłowski, L. Pacholski, & T. Wierzbicki (Eds.), Mathematical Foundations of Computer Science 1999 - 24th International Symposium, MFCS 1999, Proceedings (pp. 48-58). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 1672). Springer Verlag. https://doi.org/10.1007/3-540-48340-3_5