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Parameterized Complexity of Asynchronous Border Minimization
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 under several natural parameters. We show that BMP and P-BMP
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 (l)
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, P-BMP is in FPT when
parameterized by c and l. We complement our tractability results with
corresponding hardness results