### Abstract

We introduce a new matching criterion - function matching - that captures several different applications. The function matching problem has as its input a text T of length n over alphabet Σ _{T} and a pattern P = P[1]P[2] ⋯ P[m] of length m over alphabet Σ _{P}. We seek all text locations i for which, for some function f : Σ _{P} > Σ _{T} (f may also depend on i), the m-length substring that starts at i is equal to f(P[1])f(P[2])⋯f(P[m]). We give a randomized algorithm which, for any given constant k, solves the function matching problem in time O(n log n) with probability 1/n ^{k} of declaring a false positive. We give a deterministic algorithm whose time is O(n|Σ _{P}|log m) and show that it is almost optimal in the newly formalized convolutions model. Finally, a variant of the third problem is solved by means of two-dimensional parameterized matching, for which we also give an efficient algorithm.

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

Pages (from-to) | 929-942 |

Number of pages | 14 |

Journal | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |

Volume | 2719 |

State | Published - 2003 |

### Fingerprint

### Keywords

- Color indexing
- Function matching
- Parameterized matching
- Pattern matching
- Protein folding
- Register allocation

### ASJC Scopus subject areas

- Computer Science(all)
- Biochemistry, Genetics and Molecular Biology(all)
- Theoretical Computer Science

### Cite this

*Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)*,

*2719*, 929-942.

**Function matching : Algorithms, applications, and a lower bound.** / Amir, Amihood; Aumann, Yonatan; Cole, Richard; Lewenstein, Moshe; Porat, Ely.

Research output: Contribution to journal › Article

*Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)*, vol. 2719, pp. 929-942.

}

TY - JOUR

T1 - Function matching

T2 - Algorithms, applications, and a lower bound

AU - Amir, Amihood

AU - Aumann, Yonatan

AU - Cole, Richard

AU - Lewenstein, Moshe

AU - Porat, Ely

PY - 2003

Y1 - 2003

N2 - We introduce a new matching criterion - function matching - that captures several different applications. The function matching problem has as its input a text T of length n over alphabet Σ T and a pattern P = P[1]P[2] ⋯ P[m] of length m over alphabet Σ P. We seek all text locations i for which, for some function f : Σ P > Σ T (f may also depend on i), the m-length substring that starts at i is equal to f(P[1])f(P[2])⋯f(P[m]). We give a randomized algorithm which, for any given constant k, solves the function matching problem in time O(n log n) with probability 1/n k of declaring a false positive. We give a deterministic algorithm whose time is O(n|Σ P|log m) and show that it is almost optimal in the newly formalized convolutions model. Finally, a variant of the third problem is solved by means of two-dimensional parameterized matching, for which we also give an efficient algorithm.

AB - We introduce a new matching criterion - function matching - that captures several different applications. The function matching problem has as its input a text T of length n over alphabet Σ T and a pattern P = P[1]P[2] ⋯ P[m] of length m over alphabet Σ P. We seek all text locations i for which, for some function f : Σ P > Σ T (f may also depend on i), the m-length substring that starts at i is equal to f(P[1])f(P[2])⋯f(P[m]). We give a randomized algorithm which, for any given constant k, solves the function matching problem in time O(n log n) with probability 1/n k of declaring a false positive. We give a deterministic algorithm whose time is O(n|Σ P|log m) and show that it is almost optimal in the newly formalized convolutions model. Finally, a variant of the third problem is solved by means of two-dimensional parameterized matching, for which we also give an efficient algorithm.

KW - Color indexing

KW - Function matching

KW - Parameterized matching

KW - Pattern matching

KW - Protein folding

KW - Register allocation

UR - http://www.scopus.com/inward/record.url?scp=35248829485&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=35248829485&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:35248829485

VL - 2719

SP - 929

EP - 942

JO - Lecture Notes in Computer Science

JF - Lecture Notes in Computer Science

SN - 0302-9743

ER -