Parameterized Complexity of Asynchronous Border Minimization

  • Robert Ganian
  • Martin Kronegger
  • Andreas Pfandler
  • Alexandru Popa
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9076)


Microarrays are research tools used in gene discovery as well as disease and cancer diagnostics. Two prominent but challenging problems related to microarrays are the Border Minimization Problem (BMP) and the Border Minimization Problem with given placement (P-BMP). In this paper we investigate the parameterized complexity of natural variants of BMP and P-BMP, termed \(\mathrm{BMP}^e\) and \(\hbox {P-BMP}^{e}\) respectively, under several natural parameters. We show that \(\mathrm{BMP}^e\) and \(\hbox {P-BMP}^{e}\) are in FPT under the following two combinations of parameters: (\(1\)) the size of the alphabet (\(c\)), the maximum length of a sequence (string) in the  input (\(\ell \)) and the number of rows of the microarray (\(r\)); and, (\(2\)) the size of the alphabet and the size of the border length (\(o\)). Furthermore, \(\hbox {P-BMP}^{e}\) is in FPT when parameterized by \(c\) and \(\ell \). We complement our tractability results with corresponding hardness results.


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Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  • Robert Ganian
    • 1
  • Martin Kronegger
    • 1
  • Andreas Pfandler
    • 1
    • 2
  • Alexandru Popa
    • 3
  1. 1.Vienna University of TechnologyViennaAustria
  2. 2.University of SiegenSiegenGermany
  3. 3.Nazarbayev UniversityAstanaKazakhstan

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