We develop an hidden Markov model (HMM)-based algorithm for
computing exact parametric and non-parametric linkage scores
in larger pedigrees than was possible before. The algorithm is
applicable whenever there are chains of persons in the pedigree
with no genetic measurements and with unknown affection status.
The algorithm is based on shrinking the state space of the HMM
considerably using such chains. In a two g-degree cousins pedigree
the reduction drops the state space from being exponential in g to
being linear in g. For a Finnish family in which two affected children
suffer from a rare cold-inducing sweating syndrome, we were able to
reduce the state space by more than five orders of magnitude from
250 to 232. In another pedigree of state-space size of 227, used for a
study of pituitary adenoma, the state space reduced by a factor of
8.5 and consequently exact