### Abstract

The 2-LCPS problem, first introduced by Chowdhury et al. (2014) [17], asks one to compute (the length of) a longest common palindromic subsequence between two given strings A and B. We show that the 2-LCPS problem is at least as hard as the well-studied longest common subsequence problem for four strings. Then, we present a new algorithm which solves the 2-LCPS problem in O(σM^{2}+n) time, where n denotes the length of A and B, M denotes the number of matching positions between A and B, and σ denotes the number of distinct characters occurring in both A and B. Our new algorithm is faster than Chowdhury et al.'s sparse algorithm when σ=o(log^{2}nloglogn).

Original language | English |
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Pages (from-to) | 11-15 |

Number of pages | 5 |

Journal | Information Processing Letters |

Volume | 129 |

DOIs | |

Publication status | Published - Jan 2018 |

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### All Science Journal Classification (ASJC) codes

- Theoretical Computer Science
- Signal Processing
- Information Systems
- Computer Science Applications

### Cite this

**A hardness result and new algorithm for the longest common palindromic subsequence problem.** / Inenaga, Shunsuke; Hyyrö, Heikki.

Research output: Contribution to journal › Article

*Information Processing Letters*, vol. 129, pp. 11-15. https://doi.org/10.1016/j.ipl.2017.08.006

}

TY - JOUR

T1 - A hardness result and new algorithm for the longest common palindromic subsequence problem

AU - Inenaga, Shunsuke

AU - Hyyrö, Heikki

PY - 2018/1

Y1 - 2018/1

N2 - The 2-LCPS problem, first introduced by Chowdhury et al. (2014) [17], asks one to compute (the length of) a longest common palindromic subsequence between two given strings A and B. We show that the 2-LCPS problem is at least as hard as the well-studied longest common subsequence problem for four strings. Then, we present a new algorithm which solves the 2-LCPS problem in O(σM2+n) time, where n denotes the length of A and B, M denotes the number of matching positions between A and B, and σ denotes the number of distinct characters occurring in both A and B. Our new algorithm is faster than Chowdhury et al.'s sparse algorithm when σ=o(log2nloglogn).

AB - The 2-LCPS problem, first introduced by Chowdhury et al. (2014) [17], asks one to compute (the length of) a longest common palindromic subsequence between two given strings A and B. We show that the 2-LCPS problem is at least as hard as the well-studied longest common subsequence problem for four strings. Then, we present a new algorithm which solves the 2-LCPS problem in O(σM2+n) time, where n denotes the length of A and B, M denotes the number of matching positions between A and B, and σ denotes the number of distinct characters occurring in both A and B. Our new algorithm is faster than Chowdhury et al.'s sparse algorithm when σ=o(log2nloglogn).

UR - http://www.scopus.com/inward/record.url?scp=85029384363&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85029384363&partnerID=8YFLogxK

U2 - 10.1016/j.ipl.2017.08.006

DO - 10.1016/j.ipl.2017.08.006

M3 - Article

AN - SCOPUS:85029384363

VL - 129

SP - 11

EP - 15

JO - Information Processing Letters

JF - Information Processing Letters

SN - 0020-0190

ER -