### Abstract

In this paper, we propose a new dynamic compressed index of O(w) space for a dynamic text T, where w=O(min(zlogNlog^{∗}M,N)) is the size of the signature encoding of T, z is the size of the Lempel–Ziv77 (LZ77) factorization of T, N is the length of T, and M≥N is the maximum length of T. Our index supports searching for a pattern P in T in O(|P|f_{A}+logwlog|P|log^{∗}M(logN+log|P|log^{∗}M)+occlogN) time and insertion/deletion of a substring of length y in O((y+logNlog^{∗}M)logwlogNlog^{∗}M) time, where occ is the number of occurrences of P in T and [Formula presented]. Also, we propose a new space-efficient LZ77 factorization algorithm for a given text T, which runs in O(Nf_{A}+zlogwlog^{3}N(log^{∗}N)^{2}) time with O(w) working space.

Original language | English |
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Pages (from-to) | 116-129 |

Number of pages | 14 |

Journal | Discrete Applied Mathematics |

Volume | 274 |

DOIs | |

Publication status | Published - Mar 15 2020 |

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### All Science Journal Classification (ASJC) codes

- Discrete Mathematics and Combinatorics
- Applied Mathematics

### Cite this

*Discrete Applied Mathematics*,

*274*, 116-129. https://doi.org/10.1016/j.dam.2019.01.014