The String Barcoding Problem is NP-Hard
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The String Barcoding (SBC) problem, introduced by Rash and Gusfield (RECOMB, 2002), consists in finding a minimum set of substrings that can be used to distinguish between all members of a set of given strings. In a computational biology context, the given strings represent a set of known viruses, while the substrings can be used as probes for an hybridization experiment via microarray. Eventually, one aims at the classification of new strings (unknown viruses) through the result of the hybridization experiment. Rash and Gusfield utilized an Integer Programming approach for the solution of SBC, but they left the computational complexity of the problem as an open question. In this paper we settle the question and prove that SBC is NP-hard.
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