Algorithmic Approaches to the String Barcoding Problem

This thesis deals with a heuristic approach based on Lagrangian relaxation to the string barcoding (SB) problem, a close cousin to the well-known combinatorial set cover (SC) problem. It has recently been proven to be NP-hard and has many real-world applications, particularly in the fields of medicine and biology. Given a set of sequences over some alphabet, DNA for instance, we aim at finding a set of short sequences, so-called probes, such that we are able to identify an unknown sample sequence as one of the input sequences by determining which probes are subsequences of the sample, and which are not. The problem is twofold: the determination of all possible probes and the selection of a suitable subset of minimum cardinality. The problem has been dealt with under various other names and has in this form been introduced by Rash and Gusfield in 2002. They proposed an exact approach based on integer linear programming and the use of suffix trees to generate a complete, nonredundant set of candidate probes. We evaluated several approaches for the SB as well as the SC problem. One of the leading heuristics for the SC problem, based on Lagrangian relaxation, has been proposed by Caprara et al. in 1999. We adapted the algorithm to see if it works equally well when applied to the structurally very similar SB problem. Though the results we obtained are somewhat mixed, the heuristic shows its strength with very complex instances and delivers much better results compared to simpler heuristics.