diff --git a/figures/algo.pdf b/figures/algo.pdf new file mode 100644 index 0000000000000000000000000000000000000000..0f1821b3ffd3a2d7f1f1d9174cd21f3efb086ca3 Binary files /dev/null and b/figures/algo.pdf differ diff --git a/paper.md b/paper.md index f623bb6de82ce49e02138f33b25437cd78cb840a..286ff611888e17f7bf90bd40bcb2fa507d0d1de6 100755 --- a/paper.md +++ b/paper.md @@ -36,10 +36,13 @@ If the goal of the simulation is to approximate a continuous function with the l Such a sampling strategy would trivially speedup many simulations. One of the most significant complications here is to parallelize this algorithm, as it requires a lot of bookkeeping and planning ahead. +{#fig:algo} + #### We describe a class of algorithms relying on local criteria for sampling, which allow for easy parallelization and have a low overhead. Due to parallelization, the algorithm should be local, meaning that the information updates are only in a region around the newly calculated point. Additionally, the algorithm should also be fast in order to handle many parallel workers that calculate the function and request new points. -A simple example is greedily optimizing continuity of the sampling by selecting points according to the distance to the largest gaps in the function values. +A simple example is greedily optimizing continuity of the sampling by selecting points according to the distance to the largest gaps in the function values, as in Fig. @fig:algo. For a one-dimensional function with three points known (its boundary points and a point in the center), the following steps repeat itself: (1) keep all points $x$ sorted, where two consecutive points define an interval, (2) calculate the Euclidean distance for each interval (see $L_{1,2}$ in Fig. @fig:loss_1D),