Hardness of flip-cut problems from optical mapping

Optical Mapping is a new technology for constructing restriction maps. Associated computational problems include aligning multiple partial restriction maps into a single `consensus' restriction map, and determining the correct orientation of each molecule, which was formalized as the Exclusive Binary Flip Cut (EBFC) Problem by Muthukrishnan and Parida. Here we prove that the EBFC problem, as well as a number of its variants, are NP-Complete. We also identify another problem formalized as Binary Shift Cut (BSC) problem motivated by the fact that there might be missing fragments at the beginnings and/or the ends of the molecules, and prove it to be NP-complete. Therefore, they do not have efficient, that is, polynomial time solutions unless P = NP.