The Exemplar Breakpoint Distance for non-trivial genomes cannot be approximated

Abstract : A promising and active field of comparative genomics con- sists in comparing two genomes by establishing a one-to-one correspon- dence (i.e., a matching) between their genes. This correspondence is usu- ally chosen in order to optimize a predefined measure. One such problem is the Exemplar Breakpoint Distance problem (or EBD, for short), which asks, given two genomes modeled by signed sequences of charac- ters, to keep and match exactly one occurrence of each character in the two genomes (a process called exemplarization), so as to minimize the number of breakpoints of the resulting genomes. Bryant [6] showed that EBD is NP-complete. In this paper, we close the study of the approximation of EBD by showing that no approximation factor can be derived for EBD considering non-trivial genomes - i.e. genomes that contain duplicated genes.
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Guillaume Blin, Guillaume Fertin, Florian Sikora, Stéphane Vialette. The Exemplar Breakpoint Distance for non-trivial genomes cannot be approximated. WALCOM 2009, 2009, Kolkata, India. pp.357-368. ⟨hal-00416491⟩

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