Robert Ganian, Martin Kronegger, Andreas Pfandler and Alexandru Popa 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, termed BMP and PBMP respectively, under several natural parameters. We show that BMP and PBMP 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, PBMP is in FPT when parameterized by c and l. We complement our tractability results with corresponding hardness results.