  When both the difference between two quantities and their individual values
can be measured or computational predicted, multiple quantities can be
determined from the measurements or predictions of select individual quantities
and select pairwise differences. These measurements and predictions form a
network connecting the quantities through their differences. Here, I analyze
the optimization of such networks, where the trace ($A$-optimal), the largest
eigenvalue ($E$-optimal), or the determinant ($D$-optimal) of the covariance
matrix associated with the estimated quantities are minimized with respect to
the allocation of the measurement (or computational) cost to different
measurements (or predictions). My statistical analysis of the performance of
such optimal measurement networks -- based on large sets of simulated data --
suggests that they substantially accelerate the determination of the
quantities, and that they may be useful in applications such as the
computational prediction of binding free energies of candidate drug molecules.
