Journal article
Fast searching in packed strings
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. 6 (2) (1977) 323–350] 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 σ denote the size of the alphabet.
On a standard unit-cost word-RAM with logarithmic word size we present an algorithm using timeO(nlogσn+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/logσn) our algorithm is optimal since any algorithm must spend at least Ω((n+m)logσlogn+occ)=Ω(nlogσn+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.
Language: | English |
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Year: | 2011 |
Pages: | 49-56 |
ISSN: | 15708675 and 15708667 |
Types: | Journal article |
DOI: | 10.1016/j.jda.2010.09.003 |
ORCIDs: | Bille, Philip |