Let's say I have $N_e$ grid elements $e_i$, each with a certain computational weight $w_i$. The $w_i$ are all within an order of magnitude, but I don't know their exact value a priori. The elements are now to be distributed among $N_p$ processes, preserving their order. I can only measure the cumulative weight of all elements on one process but not their individual contributions. However, I can repartition the grid multiple times to get multiple measurements with different decompositions.
What I am searching for is a method that lets me determine an estimate for the $w_i$ with a relatively low number of decompositions $N_d$. The numbers involved here are in the range of $N_e = \mathcal{O}(10^9)$, $N_p = \mathcal{O}(10^5)$, and $N_d = \mathcal{O}(10^2)$.