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 Gusfield,
a genotype is *ambiguous* if its value
is 2; and *resolved* otherwise. Two haplotypes *h _{1}*
and

if *g*[*j*]=2 then *h _{1}*[

if *g*[*j*]=1 then *h _{1}*[

if *g*[*j*]=0 then *h _{1}*[

For
instance, the genotype `20110` can be explained by the haplotypes `10110` and `00110`:

10110

00110

-------

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 Every genotype *g* in *G* is mapped to two haplotypes in *H*.

C2 For every genotype *g* in *G*, for every
ambiguous site *j* of *g*, the values of the *j*'th sites of these haplotypes are different.

C3 For every genotype *g* in *G*, for every
resolved site *j* of *g*, the values of the *j*'th site of these haplotypes are *g*[*j*].