Table 1.

Summary of Notations

S, si, $S_i^{\prime }$	the sample set, a sample, a subset of samples
M, mi	the marker set, a marker
H	a binary matrix representing the data
Cu,v	a compatible interval of H
f(si)	phenotype value of sample si
$F(S_i^{\prime })$	the set of phenotype values of the samples in $S_i^{\prime }$
Gi(S′)	a grouping of a sample subsets S’
Tu,v	the perfect phylogeny tree of Cu,v
E(Tu,v)	the edge set of Tu,v
S(E)(Tu,v)	the set of sample subsets implied in tree Tu,v (leaf-sets)