title: 'Adaptive, tools for adaptive parallel sampling of mathematical functions'
journal: 'PeerJ'
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@@ -102,6 +101,11 @@ An example of such a polygonal remeshing method is one where the polygons align
# Design constraints and the general algorithm
#### We aim to sample low dimensional low to intermediate cost functions in parallel.
The general algorithm that we describe in this paper works best for low to intermediary cost functions.
The point suggestion step needs to happen in a single sequential process while the function execution can happen in parallel.
This means that $t_lobal}> t_\textrm{function} / N_\textrm{parallel workers} > t_\textrm{to suggest}$, in order to benefit from our adaptive sampling algorithm.
Very fast functions can be calculated on a dense grid; however, extremely slow functions might benefit from full Bayesian optimization, nonetheless a large class of functions is inside the right regime.
Further, because of the curse of dimensionality---the sparsity of space in higher dimensions---our local algorithm works best in low dimensional space; typically calculations that can reasonably be plotted.
<!-- This should explain to which domain our problem belongs. -->
