  We consider anti-phase synchronization of coupled oscillators using the
Stuart-Landau model and explore its relative infrequency in occurrence compared
to in-phase synchronization. We report effective limits in number of
oscillators which can anti-phase synchronize for general configurations of
real-world networks. We link anti-phase synchronization to the Ising model and
consequently to combinatorial optimization problems, thereby explaining
experimentally observed limits in self-organization of natural systems. We
illustrate this using the Steiner-tree problem.
