## Abstract

Inspired by a recent approach for genome reconstruction from incomplete data, we consider a variant of the longest common subsequence problem for the comparison of two sequences, one of which is incomplete, i.e. it has some missing elements. The new combinatorial problem, called Longest Filled Common Subsequence, given two sequences A and B, and a multiset M of symbols missing in B, asks for a sequence B^{∗} obtained by inserting the symbols of M into B so that B^{∗} induces a common subsequence with A of maximum length. First, we investigate the computational and approximation complexity of the problem and we show that it is NP-hard and APX-hard when A contains at most two occurrences of each symbol. Then, we give a 3/5-approximation algorithm for the problem. Finally, we present a fixed-parameter algorithm, when the problem is parameterized by the number of symbols inserted in B that "match" symbols of A.

Original language | English |
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Title of host publication | 28th Annual Symposium on Combinatorial Pattern Matching, CPM 2017 |

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

Volume | 78 |

ISBN (Electronic) | 9783959770392 |

DOIs | |

Publication status | Published - 1 Jul 2017 |

Event | 28th Annual Symposium on Combinatorial Pattern Matching, CPM 2017 - Warsaw, Poland Duration: 4 Jul 2017 → 6 Jul 2017 |

### Conference

Conference | 28th Annual Symposium on Combinatorial Pattern Matching, CPM 2017 |
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Country | Poland |

City | Warsaw |

Period | 4/07/17 → 6/07/17 |

## Keywords

- Approximation algorithms
- Computational complexity
- Fixed-parameter algorithms
- Longest common subsequence