  For families, kinship coefficients are quantifications of the amount of
genetic sharing between a pair of individuals. These coefficients are critical
for understanding the breeding habits and genetic diversity of diploid
populations. Historically, computations of the inbreeding coefficient were used
to prohibit inbred marriages and prohibit breeding of some pairs of pedigree
animals. Such prohibitions foster genetic diversity and help prevent recessive
Mendelian disease at a population level.
  This paper gives the fastest known algorithms for computing the kinship
coefficient of a set of individuals with a known pedigree. The algorithms given
here consider the possibility that the founders of the known pedigree may
themselves be inbred, and they compute the appropriate inbreeding-adjusted
kinship coefficients. The exact kinship algorithm has running-time $O(n^2)$ for
an $n$-individual pedigree. The recursive-cut exact kinship algorithm has
running time $O(s^2m)$ where $s$ is the number of individuals in the largest
segment of the pedigree and $m$ is the number of cuts. The approximate
algorithm has running-time $O(n)$ for an $n$-individual pedigree on which to
estimate the kinship coefficients of $\sqrt{n}$ individuals from $\sqrt{n}$
founder kinship coefficients.
