Tighter lower bounds on the exact complexity of string matching

Richard Cole, Ramesh Hariharan, Mike Paterson, Uri Zwick

Research output: Contribution to journalArticle

Abstract

This paper considers the exact number of character comparisons needed to find all occurrences of a pattern of length m in a text of length n using on-line and general algorithms. For on-line algorithms, a lower bound of about (1 + 9 ÷ 4(m + 1)) · n character comparisons is obtained. For general algorithms, a lower bound of about (1 + 2 ÷ m + 3) · n character comparisons is obtained. These lower bounds complement an on-line upper bound of about (1 + 8 ÷ 3(m + 1)) · n comparisons obtained recently by Cole and Hariharan. The lower bounds are obtained by finding patterns with interesting combinatorial properties. It is also shown that for some patterns off-line algorithms can be more efficient than on-line algorithms.

Original languageEnglish (US)
Pages (from-to)30-45
Number of pages16
JournalSIAM Journal on Computing
Volume24
Issue number1
StatePublished - Feb 1995

Fingerprint

String Matching
Lower bound
Complement
Upper bound
Line
Character

ASJC Scopus subject areas

  • Computational Theory and Mathematics
  • Applied Mathematics
  • Theoretical Computer Science

Cite this

Cole, R., Hariharan, R., Paterson, M., & Zwick, U. (1995). Tighter lower bounds on the exact complexity of string matching. SIAM Journal on Computing, 24(1), 30-45.

Tighter lower bounds on the exact complexity of string matching. / Cole, Richard; Hariharan, Ramesh; Paterson, Mike; Zwick, Uri.

In: SIAM Journal on Computing, Vol. 24, No. 1, 02.1995, p. 30-45.

Research output: Contribution to journalArticle

Cole, R, Hariharan, R, Paterson, M & Zwick, U 1995, 'Tighter lower bounds on the exact complexity of string matching', SIAM Journal on Computing, vol. 24, no. 1, pp. 30-45.
Cole, Richard ; Hariharan, Ramesh ; Paterson, Mike ; Zwick, Uri. / Tighter lower bounds on the exact complexity of string matching. In: SIAM Journal on Computing. 1995 ; Vol. 24, No. 1. pp. 30-45.
@article{cfcedb74336b498aae25475cb7e77efb,
title = "Tighter lower bounds on the exact complexity of string matching",
abstract = "This paper considers the exact number of character comparisons needed to find all occurrences of a pattern of length m in a text of length n using on-line and general algorithms. For on-line algorithms, a lower bound of about (1 + 9 ÷ 4(m + 1)) · n character comparisons is obtained. For general algorithms, a lower bound of about (1 + 2 ÷ m + 3) · n character comparisons is obtained. These lower bounds complement an on-line upper bound of about (1 + 8 ÷ 3(m + 1)) · n comparisons obtained recently by Cole and Hariharan. The lower bounds are obtained by finding patterns with interesting combinatorial properties. It is also shown that for some patterns off-line algorithms can be more efficient than on-line algorithms.",
author = "Richard Cole and Ramesh Hariharan and Mike Paterson and Uri Zwick",
year = "1995",
month = "2",
language = "English (US)",
volume = "24",
pages = "30--45",
journal = "SIAM Journal on Computing",
issn = "0097-5397",
publisher = "Society for Industrial and Applied Mathematics Publications",
number = "1",

}

TY - JOUR

T1 - Tighter lower bounds on the exact complexity of string matching

AU - Cole, Richard

AU - Hariharan, Ramesh

AU - Paterson, Mike

AU - Zwick, Uri

PY - 1995/2

Y1 - 1995/2

N2 - This paper considers the exact number of character comparisons needed to find all occurrences of a pattern of length m in a text of length n using on-line and general algorithms. For on-line algorithms, a lower bound of about (1 + 9 ÷ 4(m + 1)) · n character comparisons is obtained. For general algorithms, a lower bound of about (1 + 2 ÷ m + 3) · n character comparisons is obtained. These lower bounds complement an on-line upper bound of about (1 + 8 ÷ 3(m + 1)) · n comparisons obtained recently by Cole and Hariharan. The lower bounds are obtained by finding patterns with interesting combinatorial properties. It is also shown that for some patterns off-line algorithms can be more efficient than on-line algorithms.

AB - This paper considers the exact number of character comparisons needed to find all occurrences of a pattern of length m in a text of length n using on-line and general algorithms. For on-line algorithms, a lower bound of about (1 + 9 ÷ 4(m + 1)) · n character comparisons is obtained. For general algorithms, a lower bound of about (1 + 2 ÷ m + 3) · n character comparisons is obtained. These lower bounds complement an on-line upper bound of about (1 + 8 ÷ 3(m + 1)) · n comparisons obtained recently by Cole and Hariharan. The lower bounds are obtained by finding patterns with interesting combinatorial properties. It is also shown that for some patterns off-line algorithms can be more efficient than on-line algorithms.

UR - http://www.scopus.com/inward/record.url?scp=0029245659&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0029245659&partnerID=8YFLogxK

M3 - Article

VL - 24

SP - 30

EP - 45

JO - SIAM Journal on Computing

JF - SIAM Journal on Computing

SN - 0097-5397

IS - 1

ER -