An FPT-Algorithm for Longest Common Subsequence Parameterized by the Maximum Number of Deletions

Authors Laurent Bulteau , Mark Jones , Rolf Niedermeier , Till Tantau

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Author Details

Laurent Bulteau
  • LIGM, CNRS, Université Gustave Eiffel, F77454 Marne-la-vallée, France
Mark Jones
  • Delft Institute of Applied Mathematics, Delft University of Technology, The Netherlands
Rolf Niedermeier
  • Algorithmics and Computational Complexity, Faculty IV, TU Berlin, Germany
Till Tantau
  • Institute of Theoretical Computer Science, University of Lübeck, Germany


This work was initiated during Dagstuhl Seminar 19443, Algorithms and Complexity in Phylogenetics, held at Schloss Dagstuhl, Germany, in October 2019 [Magnus Bordewich et al., 2019].

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Laurent Bulteau, Mark Jones, Rolf Niedermeier, and Till Tantau. An FPT-Algorithm for Longest Common Subsequence Parameterized by the Maximum Number of Deletions. In 33rd Annual Symposium on Combinatorial Pattern Matching (CPM 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 223, pp. 6:1-6:11, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)


In the NP-hard Longest Common Subsequence problem (LCS), given a set of strings, the task is to find a string that can be obtained from every input string using as few deletions as possible. LCS is one of the most fundamental string problems with numerous applications in various areas, having gained a lot of attention in the algorithms and complexity research community. Significantly improving on an algorithm by Irving and Fraser [CPM'92], featured as a research challenge in a 2014 survey paper, we show that LCS is fixed-parameter tractable (FPT) when parameterized by the maximum number of deletions per input string. Given the relatively moderate running time of our algorithm (linear time when the parameter is a constant) and small parameter values to be expected in several applications, we believe that our purely theoretical analysis could finally pave the way to a new, exact and practically useful algorithm for this notoriously hard string problem.

Subject Classification

ACM Subject Classification
  • Theory of computation → Design and analysis of algorithms
  • Theory of computation → Theory and algorithms for application domains
  • NP-hard string problems
  • multiple sequence alignment
  • center string
  • parameterized complexity
  • search tree algorithms
  • enumerative algorithms


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