## Abstract

Text indexing is a fundamental problem in computer science, where the task is to index a given text (string) T[1..n], such that whenever a pattern P[1..p] comes as a query, we can efficiently report all those locations where P occurs as a substring of T. In this paper, we consider the case when P contains wildcard characters (which can match with any other character). The first non-trivial solution for the problem was given by Cole et al. [11], where the index space is O(nlog^{k}n) words or O(nlog^{k+1}n) bits and the query time is O(p+2^{h}loglogn+occ), where k is the maximum number of wildcard characters allowed in P, h≤k is the number of wildcard characters in P and occ represents the number of occurrences of P in T. Even though many indexes offering different space-time trade-offs were later proposed, a clear improvement on this result is still not known. In this paper, we first propose an O(nlog^{k+ε}n) bits index achieving the same query time as the of Cole et al.'s index, where 0<ε<1 is an arbitrary small constant. Then we propose another index of size O(nlog^{k}nlogσ) bits, but with a slightly higher query time of O(p+2^{h}logn+occ), where σ denotes the alphabet set size. We also study a related problem, where the task is to index a collection of documents (of n characters in total) so as to find the number of distinct documents containing a query pattern P. For the case where P contains at most a single wildcard character, we propose an O(nlog. . n)-word index with optimal O(p) query time.

Original language | English |
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Pages (from-to) | 120-127 |

Number of pages | 8 |

Journal | Theoretical Computer Science |

Volume | 557 |

Issue number | C |

DOIs | |

State | Published - 2014 |

### Bibliographical note

Publisher Copyright:© 2014.

## Keywords

- Data structures
- Range searching
- String indexing
- Suffix trees
- Wildcards