  We present a framework for the design of optimal assembly algorithms for
shotgun sequencing under the criterion of complete reconstruction. We derive a
lower bound on the read length and the coverage depth required for
reconstruction in terms of the repeat statistics of the genome. Building on
earlier works, we design a de Brujin graph based assembly algorithm which can
achieve very close to the lower bound for repeat statistics of a wide range of
sequenced genomes, including the GAGE datasets. The results are based on a set
of necessary and sufficient conditions on the DNA sequence and the reads for
reconstruction. The conditions can be viewed as the shotgun sequencing analogue
of Ukkonen-Pevzner's necessary and sufficient conditions for Sequencing by
Hybridization.
