Fast Searching in Packed Strings

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    Abstract

    Given strings P and Q the (exact) string matching problem is to find all positions of substrings in Q matching P. The classical Knuth-Morris-Pratt algorithm [SIAM J. Comput., 1977] solves the string matching problem in linear time which is optimal if we can only read one character at the time. However, most strings are stored in a computer in a packed representation with several characters in a single word, giving us the opportunity to read multiple characters simultaneously. In this paper we study the worst-case complexity of string matching on strings given in packed representation. Let m <= n be the lengths P and Q, respectively, and let sigma denote the size of the alphabet. On a standard unit-cost word-RAM with logarithmic word size we present an algorithm using time

    O(n/log(sigma) n + m + occ)

    Here occ is the number of occurrences of P in Q. For m = o(n) this improves the O(n) bound of the Knuth-Morris-Pratt algorithm. Furthermore, if m = O(n/log(sigma) n) our algorithm is optimal since any algorithm must spend at least Omega((n+m) log sigma/log n + occ) = Omega(n/log sigma(n)/ + occ) time to read the input and report all occurrences. The result is obtained by a novel automaton construction based on the Knuth-Morris-Pratt algorithm combined with a new compact representation of subautomata allowing an optimal tabulation-based simulation.
    Original languageEnglish
    Title of host publicationCombinatorial Pattern Matching
    Publication date2009
    Pages116-126
    ISBN (Print)978-3-642-02440-5
    DOIs
    Publication statusPublished - 2009
    Event20th Annual Symposium on Combinatorial Pattern Matching - Lille, France
    Duration: 22 Jun 200924 Jun 2009
    Conference number: 20

    Conference

    Conference20th Annual Symposium on Combinatorial Pattern Matching
    Number20
    CountryFrance
    CityLille
    Period22/06/200924/06/2009
    SeriesLecture Notes in Computer Science
    Volume5577
    ISSN0302-9743

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