We view a
genotype as a vector of sites, each site having a value from the domain {0, 1,
2}; and a haplotype as a vector of sites, each site having a value from the
domain {0, 1}. According to Brown, a genotype is ambiguous if its value is 1; and resolved otherwise. Two haplotypes h1 and h2
form (or explain) a genotype g if
for every site j the following hold:
g[j] = h1[j]+ h2[j]
For
instance, the genotype 20110 can be explained by the haplotypes 10010 and 10100:
10010
10100
-------
20110
Consider a
set H of k haplotypes. For the problem above, H is a solution to HIPP-DEC if the following constraints are
satisfied:
C1' For every genotype g in G, there exist two
haplotypes h1 and h2 in H such that, for every site j,
g[j]
= h1[j]+ h2[j].