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A QPTAS for Gapless MEC

Authors: Shilpa Garg and Tobias Mömke

Published in: LIPIcs, Volume 112, 26th Annual European Symposium on Algorithms (ESA 2018)

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).

Cite as

Shilpa Garg and Tobias Mömke. A QPTAS for Gapless MEC. In 26th Annual European Symposium on Algorithms (ESA 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 112, pp. 34:1-34:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)

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  author =	{Garg, Shilpa and M\"{o}mke, Tobias},
  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 =	{Azar, Yossi and Bast, Hannah and Herman, Grzegorz},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ESA.2018.34},
  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}
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