  We introduce a new algorithm called {\sc Rec-Gen} for reconstructing the
genealogy or \textit{pedigree} of an extant population purely from its genetic
data. We justify our approach by giving a mathematical proof of the
effectiveness of {\sc Rec-Gen} when applied to pedigrees from an idealized
generative model that replicates some of the features of real-world pedigrees.
Our algorithm is iterative and provides an accurate reconstruction of a large
fraction of the pedigree while having relatively low \emph{sample complexity},
measured in terms of the length of the genetic sequences of the population. We
propose our approach as a prototype for further investigation of the pedigree
reconstruction problem toward the goal of applications to real-world examples.
As such, our results have some conceptual bearing on the increasingly important
issue of genomic privacy.
