### Abstract

In standard string matching, each symbol matches only itself, In other string matching problems, e.g., the string matching with “don’t-cares” problem, a symbol may match several symbols. In general, an arbitrary many-to-many matching relation might hold between symbols. We consider a general string matching problem in which such a matching relation is specified and those positions in a text t, of length n, are sought at which the pattern p, of length m, matches under this relation. Depending upon the existence of a simple and easily recognizable property in the given matching relation, we show that string matching either requires linear (i.e., O(n + m)) time or is at least as hard as boolean convolution. As an application, we show that the matching relations of several independently studied string matching problems do indeed fall into the latter (hard) category. We also give a generic string matching algorithm that works far any matching relation and has complexity o(nm) except for very “large” matching relations.

Original language | English (US) |
---|---|

Pages (from-to) | 140-148 |

Number of pages | 9 |

Journal | Information and Computation |

Volume | 122 |

Issue number | 1 |

DOIs | |

State | Published - Jan 1 1995 |

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### ASJC Scopus subject areas

- Theoretical Computer Science
- Information Systems
- Computer Science Applications
- Computational Theory and Mathematics

### Cite this

*Information and Computation*,

*122*(1), 140-148. https://doi.org/10.1006/inco.1995.1144

**String matching under a general matching relation.** / Muthukrishnan, Shanmugavelayutham; Ramesh, H.

Research output: Contribution to journal › Article

*Information and Computation*, vol. 122, no. 1, pp. 140-148. https://doi.org/10.1006/inco.1995.1144

}

TY - JOUR

T1 - String matching under a general matching relation

AU - Muthukrishnan, Shanmugavelayutham

AU - Ramesh, H.

PY - 1995/1/1

Y1 - 1995/1/1

N2 - In standard string matching, each symbol matches only itself, In other string matching problems, e.g., the string matching with “don’t-cares” problem, a symbol may match several symbols. In general, an arbitrary many-to-many matching relation might hold between symbols. We consider a general string matching problem in which such a matching relation is specified and those positions in a text t, of length n, are sought at which the pattern p, of length m, matches under this relation. Depending upon the existence of a simple and easily recognizable property in the given matching relation, we show that string matching either requires linear (i.e., O(n + m)) time or is at least as hard as boolean convolution. As an application, we show that the matching relations of several independently studied string matching problems do indeed fall into the latter (hard) category. We also give a generic string matching algorithm that works far any matching relation and has complexity o(nm) except for very “large” matching relations.

AB - In standard string matching, each symbol matches only itself, In other string matching problems, e.g., the string matching with “don’t-cares” problem, a symbol may match several symbols. In general, an arbitrary many-to-many matching relation might hold between symbols. We consider a general string matching problem in which such a matching relation is specified and those positions in a text t, of length n, are sought at which the pattern p, of length m, matches under this relation. Depending upon the existence of a simple and easily recognizable property in the given matching relation, we show that string matching either requires linear (i.e., O(n + m)) time or is at least as hard as boolean convolution. As an application, we show that the matching relations of several independently studied string matching problems do indeed fall into the latter (hard) category. We also give a generic string matching algorithm that works far any matching relation and has complexity o(nm) except for very “large” matching relations.

UR - http://www.scopus.com/inward/record.url?scp=0000868653&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0000868653&partnerID=8YFLogxK

U2 - 10.1006/inco.1995.1144

DO - 10.1006/inco.1995.1144

M3 - Article

AN - SCOPUS:0000868653

VL - 122

SP - 140

EP - 148

JO - Information and Computation

JF - Information and Computation

SN - 0890-5401

IS - 1

ER -