License: Creative Commons Attribution 3.0 Unported license (CC BY 3.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.ESA.2018.34
URN: urn:nbn:de:0030-drops-94978
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Garg, Shilpa ; Mömke, Tobias

A QPTAS for Gapless MEC

LIPIcs-ESA-2018-34.pdf (0.5 MB)


We consider the problem Minimum Error Correction (MEC). A MEC instance is an n x m matrix M with entries from {0,1,-}. Feasible solutions are composed of two binary m-bit strings, together with an assignment of each row of M to one of the two strings. The objective is to minimize the number of mismatches (errors) where the row has a value that differs from the assigned solution string. The symbol "-" is a wildcard that matches both 0 and 1. A MEC instance is gapless, if in each row of M all binary entries are consecutive.
Gapless-MEC is a relevant problem in computational biology, and it is closely related to segmentation problems that were introduced by {[}Kleinberg-Papadimitriou-Raghavan STOC'98{]} in the context of data mining.
Without restrictions, it is known to be UG-hard to compute an O(1)-approximate solution to MEC. For both MEC and Gapless-MEC, the best polynomial time approximation algorithm has a logarithmic performance guarantee. We partially settle the approximation status of Gapless-MEC by providing a quasi-polynomial time approximation scheme (QPTAS). Additionally, for the relevant case where the binary part of a row is not contained in the binary part of another row, we provide a polynomial time approximation scheme (PTAS).

BibTeX - Entry

  author =	{Shilpa Garg and Tobias M{\"o}mke},
  title =	{{A QPTAS for Gapless MEC}},
  booktitle =	{26th Annual European Symposium on Algorithms (ESA 2018)},
  pages =	{34:1--34:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-081-1},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{112},
  editor =	{Yossi Azar and Hannah Bast and Grzegorz Herman},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{},
  URN =		{urn:nbn:de:0030-drops-94978},
  doi =		{10.4230/LIPIcs.ESA.2018.34},
  annote =	{Keywords: approximation algorithms, QPTAS, minimum error correction, segmentation, computational biology}

Keywords: approximation algorithms, QPTAS, minimum error correction, segmentation, computational biology
Collection: 26th Annual European Symposium on Algorithms (ESA 2018)
Issue Date: 2018
Date of publication: 14.08.2018

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