### Abstract

At CPM 2017, Castelli et al. define and study a new variant of the Longest Common Subsequence Problem, termed the Longest Filled Common Subsequence Problem (LFCS). For the LFCS problem, the input consists of two strings A and B and a multiset of characters M. The goal is to insert the characters from M into the string B, thus obtaining a new string B, such that the Longest Common Subsequence (LCS) between A and B∗ is maximized. Casteli et al. show that the problem is NP-hard and provide a 3/5-approximation algorithm for the problem. In this paper we study the problem from the experimental point of view. We introduce, implement and test new heuristic algorithms and compare them with the approximation algorithm of Casteli et al. Moreover, we introduce an Integer Linear Program (ILP) model for the problem and we use the state of the art ILP solver, Gurobi, to obtain exact solution for moderate sized instances.

Original language | English |
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Title of host publication | Proceedings - 2018 20th International Symposium on Symbolic and Numeric Algorithms for Scientific Computing, SYNASC 2018 |

Publisher | Institute of Electrical and Electronics Engineers Inc. |

Pages | 449-453 |

Number of pages | 5 |

ISBN (Electronic) | 9781728106250 |

DOIs | |

Publication status | Published - Sep 1 2018 |

Event | 20th International Symposium on Symbolic and Numeric Algorithms for Scientific Computing, SYNASC 2018 - Timisoara, Romania Duration: Sep 20 2018 → Sep 23 2018 |

### Publication series

Name | Proceedings - 2018 20th International Symposium on Symbolic and Numeric Algorithms for Scientific Computing, SYNASC 2018 |
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### Conference

Conference | 20th International Symposium on Symbolic and Numeric Algorithms for Scientific Computing, SYNASC 2018 |
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Country | Romania |

City | Timisoara |

Period | 9/20/18 → 9/23/18 |

### Fingerprint

### Keywords

- Heuristic
- Longest common subsequence
- NP-hard problem

### ASJC Scopus subject areas

- Computational Theory and Mathematics
- Software
- Computational Mathematics
- Modelling and Simulation
- Numerical Analysis

### Cite this

*Proceedings - 2018 20th International Symposium on Symbolic and Numeric Algorithms for Scientific Computing, SYNASC 2018*(pp. 449-453). [8750767] (Proceedings - 2018 20th International Symposium on Symbolic and Numeric Algorithms for Scientific Computing, SYNASC 2018). Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/SYNASC.2018.00075

**Heuristic algorithms for the longest filled common subsequence problem.** / Mincu, Radu Stefan; Popa, Alexandru.

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

*Proceedings - 2018 20th International Symposium on Symbolic and Numeric Algorithms for Scientific Computing, SYNASC 2018.*, 8750767, Proceedings - 2018 20th International Symposium on Symbolic and Numeric Algorithms for Scientific Computing, SYNASC 2018, Institute of Electrical and Electronics Engineers Inc., pp. 449-453, 20th International Symposium on Symbolic and Numeric Algorithms for Scientific Computing, SYNASC 2018, Timisoara, Romania, 9/20/18. https://doi.org/10.1109/SYNASC.2018.00075

}

TY - GEN

T1 - Heuristic algorithms for the longest filled common subsequence problem

AU - Mincu, Radu Stefan

AU - Popa, Alexandru

PY - 2018/9/1

Y1 - 2018/9/1

N2 - At CPM 2017, Castelli et al. define and study a new variant of the Longest Common Subsequence Problem, termed the Longest Filled Common Subsequence Problem (LFCS). For the LFCS problem, the input consists of two strings A and B and a multiset of characters M. The goal is to insert the characters from M into the string B, thus obtaining a new string B, such that the Longest Common Subsequence (LCS) between A and B∗ is maximized. Casteli et al. show that the problem is NP-hard and provide a 3/5-approximation algorithm for the problem. In this paper we study the problem from the experimental point of view. We introduce, implement and test new heuristic algorithms and compare them with the approximation algorithm of Casteli et al. Moreover, we introduce an Integer Linear Program (ILP) model for the problem and we use the state of the art ILP solver, Gurobi, to obtain exact solution for moderate sized instances.

AB - At CPM 2017, Castelli et al. define and study a new variant of the Longest Common Subsequence Problem, termed the Longest Filled Common Subsequence Problem (LFCS). For the LFCS problem, the input consists of two strings A and B and a multiset of characters M. The goal is to insert the characters from M into the string B, thus obtaining a new string B, such that the Longest Common Subsequence (LCS) between A and B∗ is maximized. Casteli et al. show that the problem is NP-hard and provide a 3/5-approximation algorithm for the problem. In this paper we study the problem from the experimental point of view. We introduce, implement and test new heuristic algorithms and compare them with the approximation algorithm of Casteli et al. Moreover, we introduce an Integer Linear Program (ILP) model for the problem and we use the state of the art ILP solver, Gurobi, to obtain exact solution for moderate sized instances.

KW - Heuristic

KW - Longest common subsequence

KW - NP-hard problem

UR - http://www.scopus.com/inward/record.url?scp=85069542444&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85069542444&partnerID=8YFLogxK

U2 - 10.1109/SYNASC.2018.00075

DO - 10.1109/SYNASC.2018.00075

M3 - Conference contribution

AN - SCOPUS:85069542444

T3 - Proceedings - 2018 20th International Symposium on Symbolic and Numeric Algorithms for Scientific Computing, SYNASC 2018

SP - 449

EP - 453

BT - Proceedings - 2018 20th International Symposium on Symbolic and Numeric Algorithms for Scientific Computing, SYNASC 2018

PB - Institute of Electrical and Electronics Engineers Inc.

ER -