  Structural variants compose the majority of human genetic variation, but are
difficult to assess using current genomic sequencing technologies. Optical
mapping technologies, which measure the size of chromosomal fragments between
labeled markers, offer an alternative approach. As these technologies mature
towards becoming clinical tools, there is a need to develop an approach for
determining the optimal strategy for sampling biological material in order to
detect a variant at some threshold. Here we develop an optimization approach
using a simple, yet realistic, model of the genomic mapping process using a
hyper-geometric distribution and {probabilistic} concentration inequalities.
Our approach is both computationally and analytically tractable and includes a
novel approach to getting tail bounds of hyper-geometric distribution. We show
that if a genomic mapping technology can sample most of the chromosomal
fragments within a sample, comparatively little biological material is needed
to detect a variant at high confidence.
