  Computational intractability has for decades motivated the development of a
plethora of methodologies that mainly aimed at a quality-time trade-off. The
use of Machine Learning techniques has finally emerged as one of the possible
tools to obtain approximate solutions to ${\cal NP}$-hard combinatorial
optimization problems. In a recent article, Dai et al. introduced a method for
computing such approximate solutions for instances of the Vertex Cover problem.
In this paper we consider the effectiveness of selecting a proper training
strategy by considering special problem instances called "obstructions" that we
believe carry some intrinsic properties of the problem itself. Capitalizing on
the recent work of Dai et al. on the Vertex Cover problem, and using the same
case study as well as 19 other problem instances, we show the utility of using
obstructions for training neural networks. Experiments show that training with
obstructions results in a huge reduction in number of iterations needed for
convergence, thus gaining a substantial reduction in the time needed for
training the model.
