Integer linear programming approaches for non-unique probe selection.

In addition to their prevalent use for analyzing gene expression, DNA microarrays are an efficient tool for biological, medical, and industrial applications because of their ability to assess the presence or absence of biological agents, the targets, in a sample. Given a collection of genetic sequences of targets one faces the challenge of finding short oligonucleotides, the probes, which allow detection of targets in a sample by hybridization experiments. The experiments are conducted using either unique or non-unique probes, and the problem at hand is to compute a minimal design, i.e., a minimal set of probes that allows to infer the targets in the sample from the hybridization results. If we allow to test for more than one target in the sample, the design of the probe set becomes difficult in the case of non-unique probes. Building upon previous work on group testing for microarrays we describe the first approach to select a minimal probe set for the case of non-unique probes in the presence of a small number of multiple targets in the sample. The approach is based on an integer linear programming formulation and a branch-and-cut algorithm. Our implementation significantly reduces the number of probes needed while preserving the decoding capabilities of existing approaches