Physical Mapping is a central problem in molecular biology ... and the human genome project. The problem is to reconstruct the relative position of fragments of DNA along the genome from information on their pairwise overlaps. We show that four simplified models of the problem lead to NP-complete decision problems: Colored unit interval graph completion, the maximum interval (or unit interval) subgraph, the pathwidth of a bipartite graph, and the k-consecutive ones problem for k >= 2. These models have been chosen to reflect various features typical in biological data, including false negative and positive errors, small width of the map and chimericism.

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.