Inapproximability of (1,2)-Exemplar Distance

International audienceGiven two genomes possibly with duplicate genes, the exemplar distance problem is that of removing all but one copy of each gene in each genome, so as to minimize the distance between the two reduced genomes according to some measure. Let (s, t)-Exemplar Distance denote the exemplar distance problem on two genomes G1 and G2 where each gene occurs at most s times in G1 and at most t times in G2. We show that the simplest non-trivial variant of the exemplar distance problem, (1,2)-Exemplar Distance, is already hard to approximate for a wide variety of distance measures, including popular genome rearrangement measures such as adjacency disruptions and signed reversals, and classic string edit distance measures such as Levenshtein and Hamming distance