Work-time optimal parallel prefix matching

Leszek Gąsieniec, Kunsoo Park

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

5 Scopus citations


Consider the prefix matching problem: Given a pattern P of length m and a text T of length n, find for all positions i in T the longest prefix of P starting at i. We present a parallel algorithm for the prefix matching problem over general alphabets whose text search takes optimal O(α(m)) time and preprocessing takes optimal O(log log m) time, where α(m) is the inverse Ackermann function. An Ω(log log m) lower bound for the prefix matching problem is implied by the same lower bound for string matching. However, the lower bound is applied only to preprocessing of the pattern and the searching phase can be faster. We prove an Ω(α(m)) lower bound for any linear-work searching phase. Therefore our algorithm is work-time optimal in both preprocessing and text search. The idea of leftmost witnesses is introduced to obtain the algorithm.

Original languageEnglish (US)
Title of host publicationAlgorithms - ESA'94 - 2nd Annual European Symposium, Proceedings
EditorsJan van Leeuwen
PublisherSpringer Verlag
Number of pages12
ISBN (Print)9783540584346
StatePublished - Jan 1 1994
Externally publishedYes
Event2nd Annual European Symposium on Algorithms, ESA 1994 - Utrecht, Netherlands
Duration: Sep 26 1994Sep 28 1994

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume855 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349


Conference2nd Annual European Symposium on Algorithms, ESA 1994

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computer Science(all)


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