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A QPTAS for Gapless MEC

Authors Shilpa Garg , Tobias Mömke

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Author Details

Shilpa Garg
  • Max Planck Institute for Informatics, Saarland Informatics Campus, Germany
Tobias Mömke
  • University of Bremen and Saarland University, Saarland Informatics Campus, Germany

Funding

  • Mömke, Tobias: Deutsche Forschungsgemeinschaft grant MO2889/1-1

Cite AsGet BibTex

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)
https://doi.org/10.4230/LIPIcs.ESA.2018.34

Abstract

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).

Subject Classification

ACM Subject Classification
  • Theory of computation → Approximation algorithms analysis
  • Theory of computation → Dynamic programming
Keywords
  • approximation algorithms
  • QPTAS
  • minimum error correction
  • segmentation
  • computational biology

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