In this page we present a new approach to haplotype inference under the perfect phylogeny model. Usually, this problem is known as Perfect Phylogeny Haplotype Problem (pph-problem, in short).

PPH-problem can be formally defined as follows: finding, if possible, a completion H of a given incomplete matrix such that H represents a collection of sets that has a tree representation.

Linear time algorithms that solve this problem are already
known.
However, our approach is quite different because it is based on a graph
characterization
of incomplete matrices.
More precisely, we define a partial order among columns of incomplete
matrices such that satisfies specific properties.
The construction of the poset proceeds incrementally and led, if the
input matrix
admits a tree completion, to a graph containing every possible
completion of the matrix.
Finally, a completion can be obtained in linear time from the
given graph.

A reference implementation of the algorithm and some examples of input data are given here.