  We consider a facility location game in which $n$ agents reside at known
locations on a path, and $k$ heterogeneous facilities are to be constructed on
the path. Each agent is adversely affected by some subset of the facilities,
and is unaffected by the others. We design two classes of mechanisms for
choosing the facility locations given the reported agent preferences:
utilitarian mechanisms that strive to maximize social welfare (i.e., to be
efficient), and egalitarian mechanisms that strive to maximize the minimum
welfare. For the utilitarian objective, we present a weakly group-strategyproof
efficient mechanism for up to three facilities, we give strongly
group-strategyproof mechanisms that achieve approximation ratios of $5/3$ and
$2$ for $k=1$ and $k > 1$, respectively, and we prove that no strongly
group-strategyproof mechanism achieves an approximation ratio less than $5/3$
for the case of a single facility. For the egalitarian objective, we present a
strategyproof egalitarian mechanism for arbitrary $k$, and we prove that no
weakly group-strategyproof mechanism achieves a $o(\sqrt{n})$ approximation
ratio for two facilities. We extend our egalitarian results to the case where
the agents are located on a cycle, and we extend our first egalitarian result
to the case where the agents are located in the unit square.
