On the border length minimization problem (BLMP) on a square array
Proceedings of the First ACM International Conference on Bioinformatics and Computational Biology
Hardness and approximation of the asynchronous border minimization problem
TAMC'12 Proceedings of the 9th Annual international conference on Theory and Applications of Models of Computation
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DNA microarray technology has proven to be an invaluable tool for molecular biologists. Microarrays are used extensively in SNP detection, genomic hybridization, alternative splicing and gene expression profiling. However the manufacturers of the microarrays are often stuck with the problem of minimizing the effects of unwanted illumination (border length minimization (BLM)) which is a hard combinatorial problem. In this paper we prove that the BLM problem on a rectangular grid is NP-hard. We also give the first integer linear programming (ILP) formulation to solve BLM problem optimally. Experimental results indicate that our ILP method produces superior results (both in runtime and cost) compared to the current state of the art algorithms to solve the BLM problem optimally.