License: Creative Commons Attribution 4.0 International license (CC BY 4.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.CPM.2022.6
URN: urn:nbn:de:0030-drops-161338
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2022/16133/
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Bulteau, Laurent ; Jones, Mark ; Niedermeier, Rolf ; Tantau, Till

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

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LIPIcs-CPM-2022-6.pdf (0.8 MB)

Abstract

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.

BibTeX - Entry

@InProceedings{bulteau_et_al:LIPIcs.CPM.2022.6,
  author =	{Bulteau, Laurent and Jones, Mark and Niedermeier, Rolf and Tantau, Till},
  title =	{{An FPT-Algorithm for Longest Common Subsequence Parameterized by the Maximum Number of Deletions}},
  booktitle =	{33rd Annual Symposium on Combinatorial Pattern Matching (CPM 2022)},
  pages =	{6:1--6:11},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-234-1},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{223},
  editor =	{Bannai, Hideo and Holub, Jan},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/opus/volltexte/2022/16133},
  URN =		{urn:nbn:de:0030-drops-161338},
  doi =		{10.4230/LIPIcs.CPM.2022.6},
  annote =	{Keywords: NP-hard string problems, multiple sequence alignment, center string, parameterized complexity, search tree algorithms, enumerative algorithms}
}

Keywords: NP-hard string problems, multiple sequence alignment, center string, parameterized complexity, search tree algorithms, enumerative algorithms
Collection: 33rd Annual Symposium on Combinatorial Pattern Matching (CPM 2022)
Issue Date: 2022
Date of publication: 22.06.2022

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