  In this paper, we consider approximability issues of the following four
problems: triangle packing, full sibling reconstruction, maximum profit
coverage and 2-coverage. All of them are generalized or specialized versions of
set-cover and have applications in biology ranging from full-sibling
reconstructions in wild populations to biomolecular clusterings; however, as
this paper shows, their approximability properties differ considerably. Our
inapproximability constant for the triangle packing problem improves upon the
previous results; this is done by directly transforming the inapproximability
gap of Haastad for the problem of maximizing the number of satisfied equations
for a set of equations over GF(2) and is interesting in its own right. Our
approximability results on the full siblings reconstruction problems answers
questions originally posed by Berger-Wolf et al. and our results on the maximum
profit coverage problem provides almost matching upper and lower bounds on the
approximation ratio, answering a question posed by Hassin and Or.
