  We study optimal synchronization in networks of heterogeneous phase
oscillators. Our main result is the derivation of a synchrony alignment
function that encodes the interplay between network structure and oscillators'
frequencies and can be readily optimized. We highlight its utility in two
general problems: constrained frequency allocation and network design. In
general, we find that synchronization is promoted by strong alignments between
frequencies and the dominant Laplacian eigenvectors, as well as a matching
between the heterogeneity of frequencies and network structure.
