Exact Algorithms for the Bounded Repetition Longest Common Subsequence Problem

Yuichi Asahiro, Jesper Andreas Jansson, Guohui Lin, Eiji Miyano, Hirotaka Ono, Tadatoshi Utashima

Research output: Chapter in book / Conference proceedingConference article published in proceeding or bookAcademic researchpeer-review


In this paper, we study exact, exponential-time algorithms for a variant of the classic Longest Common Subsequence problem called the r-Repetition Longest Common Subsequence problem (or r-RLCS, for short): Given two sequences X and Y over an alphabet S, find a longest common subsequence of X and Y such that each symbol appears at most r times in the obtained subsequence. Without loss of generality, we will assume that from here on. The special case of 1-RLCS, also known as the Repetition-Free Longest Common Subsequence problem (RFLCS), has been studied previously; e.g., in [1], Adi et al. presented an (exponential-time) integer linear programming-based exact algorithm for 1-RLCS. However, they did not analyze its time complexity, and to the best of our knowledge, there are no previous results on the running times of any exact algorithms for this problem. In this paper, we first propose a simple algorithm for 1-RLCS based on the strategy used in [1] and show explicitly that its running time is bounded by. Next, we provide a DP-based algorithm for r-RLCS and prove that its running time is for any. In particular, our new algorithm runs in time for 1-RLCS, which is faster than the previous one.

Original languageEnglish
Title of host publicationCombinatorial Optimization and Applications - 13th International Conference, COCOA 2019, Proceedings
EditorsYingshu Li, Mihaela Cardei, Yan Huang
Number of pages12
ISBN (Print)9783030364113
Publication statusPublished - 1 Jan 2019
Event13th Annual International Conference on Combinatorial Optimization and Applications, COCOA 2019 - Xiamen, China
Duration: 13 Dec 201915 Dec 2019

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume11949 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349


Conference13th Annual International Conference on Combinatorial Optimization and Applications, COCOA 2019

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computer Science(all)

Cite this