  The coupling of some types of oscillators requires the mediation of a
physical link between them, rendering the distance between oscillators a
critical factor to achieve synchronization. In this paper we propose and
explore a greedy algorithm to grow spatially embedded oscillator networks. The
algorithm is constructed in such a way that nodes are sequentially added
seeking to minimize the cost of the added links' length and optimize the linear
stability of the growing network. We show that, for appropriate parameters, the
stability of the resulting network, measured in terms of the dynamics of small
perturbations and the correlation length of the disturbances, can be
significantly improved with a minimal added length cost. In addition, we
analyze numerically the topological properties of the resulting networks and
find that, while being more stable, their degree distribution is approximately
exponential and independent of the algorithm parameters. Moreover, we find that
other topological parameters related with network resilience and efficiency are
also affected by the proposed algorithm. Finally, we extend our findings to
more general classes of networks with different sources of heterogeneity. Our
results are a first step in the development of algorithms for the directed
growth of oscillatory networks with desirable stability, dynamical and
topological properties.
