Longest Common Subsequence on Weighted Sequences

Authors Evangelos Kipouridis , Kostas Tsichlas

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Author Details

Evangelos Kipouridis
  • Basic Algorithms Research Copenhagen (BARC), University of Copenhagen, Denmark
Kostas Tsichlas
  • Computer Engineering and Informatics Department, University of Patras, Greece


We would like to thank the anonymous reviewers for their careful reading of our paper and their many insightful comments and suggestions.

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Evangelos Kipouridis and Kostas Tsichlas. Longest Common Subsequence on Weighted Sequences. In 31st Annual Symposium on Combinatorial Pattern Matching (CPM 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 161, pp. 19:1-19:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)


We consider the general problem of the Longest Common Subsequence (LCS) on weighted sequences. Weighted sequences are an extension of classical strings, where in each position every letter of the alphabet may occur with some probability. Previous results presented a PTAS and noticed that no FPTAS is possible unless P=NP. In this paper we essentially close the gap between upper and lower bounds by improving both. First of all, we provide an EPTAS for bounded alphabets (which is the most natural case), and prove that there does not exist any EPTAS for unbounded alphabets unless FPT=W[1]. Furthermore, under the Exponential Time Hypothesis, we provide a lower bound which shows that no significantly better PTAS can exist for unbounded alphabets. As a side note, we prove that it is sufficient to work with only one threshold in the general variant of the problem.

Subject Classification

ACM Subject Classification
  • Theory of computation → Approximation algorithms analysis
  • Theory of computation → W hierarchy
  • Theory of computation → Problems, reductions and completeness
  • WLCS
  • LCS
  • weighted sequences
  • approximation algorithms
  • lower bound


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