  It has been proved that the spanning tree from a given network has the
optimal synchronizability, which means the index $R=\lambda_{N}/\lambda_{2}$
reaches the minimum 1. Although the optimal synchronizability is corresponding
to the minimal critical overall coupling strength to reach synchronization, it
does not guarantee a shorter converging time from disorder initial
configuration to synchronized state. In this letter, we find that it is the
depth of the tree that affects the converging time. In addition, we present a
simple and universal way to get such an effective oriented tree in a given
network to reduce the converging time significantly by minimizing the depth of
the tree. The shortest spanning tree has both the maximal synchronizability and
efficiency.
