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DOI: 10.4230/LIPIcs.CPM.2017.14
URN: urn:nbn:de:0030-drops-73293
URL: http://drops.dagstuhl.de/opus/volltexte/2017/7329/
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Castelli, Mauro ; Dondi, Riccardo ; Mauri, Giancarlo ; Zoppis, Italo

The Longest Filled Common Subsequence Problem

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LIPIcs-CPM-2017-14.pdf (0.6 MB)


Abstract

Inspired by a recent approach for genome reconstruction from incomplete data, we consider a variant of the longest common subsequence problem for the comparison of two sequences, one of which is incomplete, i.e. it has some missing elements. The new combinatorial problem, called Longest Filled Common Subsequence, given two sequences A and B, and a multiset M of symbols missing in B, asks for a sequence B* obtained by inserting the symbols of M into B so that B* induces a common subsequence with A of maximum length. First, we investigate the computational and approximation complexity of the problem and we show that it is NP-hard and APX-hard when A contains at most two occurrences of each symbol. Then, we give a 3/5 approximation algorithm for the problem. Finally, we present a fixed-parameter algorithm, when the problem is parameterized by the number of symbols inserted in B that "match" symbols of A.

BibTeX - Entry

@InProceedings{castelli_et_al:LIPIcs:2017:7329,
  author =	{Mauro Castelli and Riccardo Dondi and Giancarlo Mauri and Italo Zoppis},
  title =	{{The Longest Filled Common Subsequence Problem}},
  booktitle =	{28th Annual Symposium on Combinatorial Pattern Matching (CPM 2017)},
  pages =	{14:1--14:13},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-039-2},
  ISSN =	{1868-8969},
  year =	{2017},
  volume =	{78},
  editor =	{Juha K{\"a}rkk{\"a}inen and Jakub Radoszewski and Wojciech Rytter},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2017/7329},
  URN =		{urn:nbn:de:0030-drops-73293},
  doi =		{10.4230/LIPIcs.CPM.2017.14},
  annote =	{Keywords: longest common subsequence, approximation algorithms, computational complexity, fixed-parameter algorithms}
}

Keywords: longest common subsequence, approximation algorithms, computational complexity, fixed-parameter algorithms
Seminar: 28th Annual Symposium on Combinatorial Pattern Matching (CPM 2017)
Issue Date: 2017
Date of publication: 28.06.2017


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