### Abstract

This paper considers various flavors of the following online problem: preprocess a text or collection of strings, so that given a query string p, all matches of p with the text can be reported quickly. In this paper we consider matches in which a bounded number of mismatches are allowed, or in which a bounded number of "don't care" characters are allowed. The specific problems we look at are: indexing, in which there is a single text t, and we seek locations where p matches a substring of t; dictionary queries, in which a collection of strings is given upfront, and we seek those strings which match p in their entirety; and dictionary matching, in which a collection of strings is given upfront. and we seek those substrings of a (long) p which match an original string in its entirety. These are all instances of an all-to-all matching problem, for which we provide a single solution. The performance bounds all have a similar character. For example, for the indexing problem with n = |t| and m = |p|, the query time for k substitutions is O(m + (c _{1} log n) ^{k}/ _{k!} + # matches), with a data structure of size O(n (c _{2} log n) ^{k}/ _{k!}) and a preprocessing time of O(n(c _{2} log n) ^{k}/ _{k!}), where c _{1}, C _{2} > 1 are constants. The deterministic preprocessing assumes a weakly nonuniform RAM model; this assumption is not needed if randomization is used in the preprocessing.

Original language | English (US) |
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Title of host publication | Conference Proceedings of the Annual ACM Symposium on Theory of Computing |

Pages | 91-100 |

Number of pages | 10 |

State | Published - 2004 |

Event | Proceedings of the 36th Annual ACM Symposium on Theory of Computing - Chicago, IL, United States Duration: Jun 13 2004 → Jun 15 2004 |

### Other

Other | Proceedings of the 36th Annual ACM Symposium on Theory of Computing |
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Country | United States |

City | Chicago, IL |

Period | 6/13/04 → 6/15/04 |

### Fingerprint

### Keywords

- Approximate pattern matching
- Dictionary matching
- Dictionary query
- Suffix trees
- Text indexing
- Wild-cards

### ASJC Scopus subject areas

- Software

### Cite this

*Conference Proceedings of the Annual ACM Symposium on Theory of Computing*(pp. 91-100)

**Dictionary matching and indexing with errors and don't cares.** / Cole, Richard; Gottlieb, Lee Ad; Lewenstein, Moshe.

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

*Conference Proceedings of the Annual ACM Symposium on Theory of Computing.*pp. 91-100, Proceedings of the 36th Annual ACM Symposium on Theory of Computing, Chicago, IL, United States, 6/13/04.

}

TY - GEN

T1 - Dictionary matching and indexing with errors and don't cares

AU - Cole, Richard

AU - Gottlieb, Lee Ad

AU - Lewenstein, Moshe

PY - 2004

Y1 - 2004

N2 - This paper considers various flavors of the following online problem: preprocess a text or collection of strings, so that given a query string p, all matches of p with the text can be reported quickly. In this paper we consider matches in which a bounded number of mismatches are allowed, or in which a bounded number of "don't care" characters are allowed. The specific problems we look at are: indexing, in which there is a single text t, and we seek locations where p matches a substring of t; dictionary queries, in which a collection of strings is given upfront, and we seek those strings which match p in their entirety; and dictionary matching, in which a collection of strings is given upfront. and we seek those substrings of a (long) p which match an original string in its entirety. These are all instances of an all-to-all matching problem, for which we provide a single solution. The performance bounds all have a similar character. For example, for the indexing problem with n = |t| and m = |p|, the query time for k substitutions is O(m + (c 1 log n) k/ k! + # matches), with a data structure of size O(n (c 2 log n) k/ k!) and a preprocessing time of O(n(c 2 log n) k/ k!), where c 1, C 2 > 1 are constants. The deterministic preprocessing assumes a weakly nonuniform RAM model; this assumption is not needed if randomization is used in the preprocessing.

AB - This paper considers various flavors of the following online problem: preprocess a text or collection of strings, so that given a query string p, all matches of p with the text can be reported quickly. In this paper we consider matches in which a bounded number of mismatches are allowed, or in which a bounded number of "don't care" characters are allowed. The specific problems we look at are: indexing, in which there is a single text t, and we seek locations where p matches a substring of t; dictionary queries, in which a collection of strings is given upfront, and we seek those strings which match p in their entirety; and dictionary matching, in which a collection of strings is given upfront. and we seek those substrings of a (long) p which match an original string in its entirety. These are all instances of an all-to-all matching problem, for which we provide a single solution. The performance bounds all have a similar character. For example, for the indexing problem with n = |t| and m = |p|, the query time for k substitutions is O(m + (c 1 log n) k/ k! + # matches), with a data structure of size O(n (c 2 log n) k/ k!) and a preprocessing time of O(n(c 2 log n) k/ k!), where c 1, C 2 > 1 are constants. The deterministic preprocessing assumes a weakly nonuniform RAM model; this assumption is not needed if randomization is used in the preprocessing.

KW - Approximate pattern matching

KW - Dictionary matching

KW - Dictionary query

KW - Suffix trees

KW - Text indexing

KW - Wild-cards

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M3 - Conference contribution

SP - 91

EP - 100

BT - Conference Proceedings of the Annual ACM Symposium on Theory of Computing

ER -