On problem of orienting ordered scaffolds

Introduction: There exists a number of methods that attempt to reconstruct a genome from a set of scaffolds. To do so, they (i) determine the order of scaffolds; and (ii) determine the orientation (i.e., strand of origin) of scaffolds. Some methods attempt to solve these subproblems jointly by using various types of additional data including jumping libraries, long error-prone reads, homology relationships between genomes, etc. Other methods (typically based on wet-lab experiments) can often reliably reconstruct the order of scaffolds, but may fail to impose their orientation. This inspires us to consider the special case of the problem (ii) where the order of scaffolds is given.