On the complexity of DNA physical mapping

The physical mapping problem is to reconstruct the relative position of fragments (clones) of DNA along the genome from information on their pairwise overlaps. We show that two simplified versions of the problem belong to the class of NP-complete problems, which are conjectured to be computationally intractable. In one version all clones have equal length, and in another clone lengths may be arbitrary. The proof uses tools from graph theory and complexity.