Reams of different methods have been applied on the inexact graph matching problem in the last decades. In fact, there are two disjoint groups of approaches, exhaustive search and approximate methods. The first ones guarantee that the best solution is always found while the last ones generally have a significantly reduced time complexity at the expense of accepting sub-optimal solutions. This article aims, first, at comparing the two complementary approaches. Secondly, we show that one can bridge the gap between them and that their combination can lead to improved performance, i.e. maintains the guarantee for the best solution while reducing the convergence time.