Several indicators have been recently proposed for measuring various characteristics of the tuples of a dataset -- particularly, the so-called skyline tuples, i.e., those that are not dominated by other tuples. Numeric indicators are very important as they may, e.g., provide an additional criterion to be used to rank skyline tuples and focus on a subset thereof. We concentrate on an indicator of robustness that may be measured for any skyline tuple $t$: grid resistance, i.e., how large value perturbations can be tolerated for $t$ to remain non-dominated (and thus in the skyline). The computation of this indicator typically involves one or more rounds of computation of the skyline itself or, at least, of dominance relationships. Building on recent advances in partitioning strategies allowing a parallel computation of skylines, we discuss how these strategies can be adapted to the computation of the indicator.