## Abstract

The k-mappability problem has two integers parameters m and k. For every subword of size m in a text S, we wish to report the number of indices in S in which the word occurs with at most k mismatches. The problem was lately tackled by Alzamel et al. [1]. For a text with constant alphabet S and k ϵ O(1), they present an algorithm with linear space and O(n logk+1 n) time. For the case in which k = 1 and a constant size alphabet, a faster algorithm with linear space and O(n log(n) log log(n)) time was presented in [2]. In this work, we enhance the techniques of [2] to obtain an algorithm with linear space and O(n log(n)) time for k = 1. Our algorithm removes the constraint of the alphabet being of constant size. We also present linear algorithms for the case of k = 1, |S| ϵ O(1) and m =Ω(√n).

Original language | English |
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Title of host publication | 32nd Annual Symposium on Combinatorial Pattern Matching, CPM 2021 |

Editors | Pawel Gawrychowski, Tatiana Starikovskaya |

Publisher | Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing |

ISBN (Electronic) | 9783959771863 |

DOIs | |

State | Published - 1 Jul 2021 |

Event | 32nd Annual Symposium on Combinatorial Pattern Matching, CPM 2021 - Wroclaw, Poland Duration: 5 Jul 2021 → 7 Jul 2021 |

### Publication series

Name | Leibniz International Proceedings in Informatics, LIPIcs |
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Volume | 191 |

ISSN (Print) | 1868-8969 |

### Conference

Conference | 32nd Annual Symposium on Combinatorial Pattern Matching, CPM 2021 |
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Country/Territory | Poland |

City | Wroclaw |

Period | 5/07/21 → 7/07/21 |

### Bibliographical note

Publisher Copyright:© Amihood Amir, Itai Boneh, and Eitan Kondratovsky.

### Funding

Funding Amihood Amir: Partly supported by ISF grant 1475/18, BSF grant 2018141 and the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme grant agreement No 683064. Itai Boneh: Partly supported by ISF grant 1475/75. Eitan Kondratovsky: Partly supported by ISF grant 1475/18. Amihood Amir: Partly supported by ISF grant 1475/18, BSF grant 2018141 and the European Research Council (ERC) under the European Union's Horizon 2020 research and innovation programme grant agreement No 683064 Partly supported by ISF grant 1475/75. Partly supported by ISF grant 1475/18.

Funders | Funder number |
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Horizon 2020 Framework Programme | 1475/75, 683064 |

European Commission | |

European Research Council | |

United States-Israel Binational Science Foundation | 2018141 |

Israel Science Foundation | 1475/18 |

## Keywords

- Hamming Distance
- Pattern Matching
- Suffix Array
- Suffix Tree