  Despite the recent progress in genome sequencing and assembly, many of the
currently available assembled genomes come in a draft form. Such draft genomes
consist of a large number of genomic fragments (scaffolds), whose order and/or
orientation (i.e., strand) in the genome are unknown. There exist various
scaffold assembly methods, which attempt to determine the order and orientation
of scaffolds along the genome chromosomes. Some of these methods (e.g., based
on FISH physical mapping, chromatin conformation capture, etc.) can infer the
order of scaffolds, but not necessarily their orientation. This leads to a
special case of the scaffold orientation problem (i.e., deducing the
orientation of each scaffold) with a known order of the scaffolds.
  We address the problem of orientating ordered scaffolds as an optimization
problem based on given weighted orientations of scaffolds and their pairs
(e.g., coming from pair-end sequencing reads, long reads, or homologous
relations). We formalize this problem using notion of a scaffold graph (i.e., a
graph, where vertices correspond to the assembled contigs or scaffolds and
edges represent connections between them). We prove that this problem is
NP-hard, and present a polynomial-time algorithm for solving its special case,
where orientation of each scaffold is imposed relatively to at most two other
scaffolds. We further develop an FPT algorithm for the general case of the OOS
problem.
