  We study the scheduling problem of makespan minimization while taking machine
conflicts into account. Machine conflicts arise in various settings, e.g.,
shared resources for pre- and post-processing of tasks or spatial restrictions.
In this context, each job has a blocking time before and after its processing
time, i.e., three parameters. We seek for conflict-free schedules in which the
blocking times of no two jobs intersect on conflicting machines. Given a set of
jobs, a set of machines, and a graph representing machine conflicts, the
problem SchedulingWithMachineConflicts (SMC), asks for a conflict-free schedule
of minimum makespan.
  We show that, unless $\textrm{P}=\textrm{NP}$, SMC on $m$ machines does not
allow for a $\mathcal{O}(m^{1-\varepsilon})$-approximation algorithm for any
$\varepsilon>0$, even in the case of identical jobs and every choice of fixed
positive parameters, including the unit case. Complementary, we provide
approximation algorithms when a suitable collection of independent sets is
given. Finally, we present polynomial time algorithms to solve the problem for
the case of unit jobs on special graph classes. Most prominently, we solve it
for bipartite graphs by using structural insights for conflict graphs of star
forests.
