### Abstract

The paper considers how many character comparisons are needed to find all occurrences of a pattern of length m in a text of length n. The main contribution is to show an upper bound of the form n + O(n/m) character comparisons, following preprocessing. Specifically, the authors show an upper bound of n+8/3(m+1)(n-m) character comparisons. This bound is achieved by an online algorithm which performs O(n) work in total, requires O(m) space and O(m
^{2}
) time for preprocessing. In addition the following lower bounds are shown: for online algorithms, a bound of n+11/5(m+1) (n-m) character comparisons for m = 10 + 11 k, for any integer k >or= 1, and for general algorithms, a bound of n+2(n-m)/m+3 character comparisons, for m=2 k+l, for any integer k>or=1.

Original language | English (US) |
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Title of host publication | Proceedings - 33rd Annual Symposium on Foundations of Computer Science, FOCS 1992 |

Publisher | IEEE Computer Society |

Pages | 600-609 |

Number of pages | 10 |

ISBN (Electronic) | 0818629002 |

DOIs | |

State | Published - Jan 1 1992 |

Event | 33rd Annual Symposium on Foundations of Computer Science, FOCS 1992 - Pittsburgh, United States Duration: Oct 24 1992 → Oct 27 1992 |

### Publication series

Name | Proceedings - Annual IEEE Symposium on Foundations of Computer Science, FOCS |
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Volume | 1992-October |

ISSN (Print) | 0272-5428 |

### Conference

Conference | 33rd Annual Symposium on Foundations of Computer Science, FOCS 1992 |
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Country | United States |

City | Pittsburgh |

Period | 10/24/92 → 10/27/92 |

### ASJC Scopus subject areas

- Computer Science(all)

### Cite this

*Proceedings - 33rd Annual Symposium on Foundations of Computer Science, FOCS 1992*(pp. 600-609). [267791] (Proceedings - Annual IEEE Symposium on Foundations of Computer Science, FOCS; Vol. 1992-October). IEEE Computer Society. https://doi.org/10.1109/SFCS.1992.267791

**Tighter bounds on the exact complexity of string matching.** / Cole, Richard; Hariharan, Ramesh.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

*Proceedings - 33rd Annual Symposium on Foundations of Computer Science, FOCS 1992.*, 267791, Proceedings - Annual IEEE Symposium on Foundations of Computer Science, FOCS, vol. 1992-October, IEEE Computer Society, pp. 600-609, 33rd Annual Symposium on Foundations of Computer Science, FOCS 1992, Pittsburgh, United States, 10/24/92. https://doi.org/10.1109/SFCS.1992.267791

}

TY - GEN

T1 - Tighter bounds on the exact complexity of string matching

AU - Cole, Richard

AU - Hariharan, Ramesh

PY - 1992/1/1

Y1 - 1992/1/1

N2 - The paper considers how many character comparisons are needed to find all occurrences of a pattern of length m in a text of length n. The main contribution is to show an upper bound of the form n + O(n/m) character comparisons, following preprocessing. Specifically, the authors show an upper bound of n+8/3(m+1)(n-m) character comparisons. This bound is achieved by an online algorithm which performs O(n) work in total, requires O(m) space and O(m 2 ) time for preprocessing. In addition the following lower bounds are shown: for online algorithms, a bound of n+11/5(m+1) (n-m) character comparisons for m = 10 + 11 k, for any integer k >or= 1, and for general algorithms, a bound of n+2(n-m)/m+3 character comparisons, for m=2 k+l, for any integer k>or=1.

AB - The paper considers how many character comparisons are needed to find all occurrences of a pattern of length m in a text of length n. The main contribution is to show an upper bound of the form n + O(n/m) character comparisons, following preprocessing. Specifically, the authors show an upper bound of n+8/3(m+1)(n-m) character comparisons. This bound is achieved by an online algorithm which performs O(n) work in total, requires O(m) space and O(m 2 ) time for preprocessing. In addition the following lower bounds are shown: for online algorithms, a bound of n+11/5(m+1) (n-m) character comparisons for m = 10 + 11 k, for any integer k >or= 1, and for general algorithms, a bound of n+2(n-m)/m+3 character comparisons, for m=2 k+l, for any integer k>or=1.

UR - http://www.scopus.com/inward/record.url?scp=85031321354&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85031321354&partnerID=8YFLogxK

U2 - 10.1109/SFCS.1992.267791

DO - 10.1109/SFCS.1992.267791

M3 - Conference contribution

T3 - Proceedings - Annual IEEE Symposium on Foundations of Computer Science, FOCS

SP - 600

EP - 609

BT - Proceedings - 33rd Annual Symposium on Foundations of Computer Science, FOCS 1992

PB - IEEE Computer Society

ER -