We study the problem of selecting control clones in DNA array hybridization experiments. The problem arises in the OFRG method for analyzing microbial communities. The OFRG method performs classification of rRNA gene clones using binary fingerprints created from a series of hybridization experiments, where each experiment consists of hybridizing a collection of arrayed clones with a single oligonucleotide probe. This experiment produces analog signals, one for each clone, which then need to be classified, that is, converted into binary values 1 and 0 that represent hybridization and non-hybridization events. Besides the sample clones, the array contains a number of control clones needed to calibrate the classification procedure of the hybridizationsignals. These control clones must be selected with care to optimize the classification process. We formulate this as a combinatorial optimization problem called Balanced Covering. We prove that the problem is NP-hard and we show some results on hardnessof approximation. We propose an approximation algorithm based on randomized rounding and we show that, with high probability, it approximates well the optimum. The experimental results confirm that the algorithm finds high quality control clones. The algorithm has been implemented and is publicly available as part of the software package called CloneTools.
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