  We link regularity and smoothness analysis of multivariate vector subdivision
schemes with network flow theory and with special linear optimization problems.
This connection allows us to prove the existence of what we call optimal
difference masks that posses crucial properties unifying the regularity
analysis of univariate and multivariate subdivision schemes. We also provide
efficient optimization algorithms for construction of such optimal masks.
Integrality of the corresponding optimal values leads to purely analytic proofs
of $C^k-$regularity of subdivision.
