## 2 Related Work  
Determining and analyzing regions of interest in three-dimensional (3D) data sets has been an important topic in many research fields, and has as such been explored in many related works [10; 11; 12; 13; 14; 15; 16; 17]. A commonly used technique is Adaptive Mesh Refinement (AMR) [13; 14; 15]. Using AMR, the simulated region is divided into multiple sub-regions, commonly by using a tree structure such as an octree [21]. After the simulation has been completed, important regions in the tree structure are subdivided to create even smaller sub-regions, on which more compute-intensive operations can be used to, for example, increase the accuracy or resolution of the simulation. This process can be performed recursively based on the researcher's specifications. The analysis required to calculate block-based importance metrics results in a fairly uniform data access over all data points in the simulation region. As such, the recursive, top-down AMR approach could result in redundant calculations and low cache hit rates. This notion is confirmed in related work [12], where a bottom-up approach, i.e., calculating the importance of each individual block, could achieve significantly better performance. Close to our work is a paper by [PERSON] et al. [10], in which calculated importance metrics were used to adaptively reduce unimportant blocks. The technique targets explicitly in-situ visualization and supports elementary data reduction and load balancing based on a random distribution. However, the technique only supports a single reduction strategy. Furthermore, their technique assumes that simulation data is stored as blocks, which is not the case for most simulations. For their technique to work in the general case, all simulation data first needs to be preprocessed and partitioned into blocks, which is time-consuming and increases the memory usage as two sets of the simulation data need to be maintained while performing the importance analysis. [PERSON] et al. [11] introduced an importance curve to store the derived importance of all data blocks for a time-varying data set. By analyzing the changing block importance between different time steps it would be possible to characterize temporal behaviors exhibited by simulation data. Such information could be used to make informed processing decisions, e.g., setting a time budget for the co-processing stage or saving data to permanent storage. [PERSON] et al. [12] presented a prioritization method for 3D data sets inspired by AMR. Data sets were recursively partitioned into smaller regions based on user defined importance metrics. A prioritization tree was constructed for the data set, which then could be used to identify interesting camera placements or to determine compression strategies for saving data to permanent storage. Some data sampling and summarization methods [16; 17] use importance based on entropy metrics to prioritize the reduction of unimportant data. Here, reduced subsets of the simulation data are saved to permanent storage for post-hoc analysis; more than 99% of simulation data is removed in some applications [16]. Data sampling methods are not suited for applications that operate on lossless simulation data. Moreover, these methods do not support use cases that require custom metrics to define important data. Table 1 shows a qualitative comparison to related work. Here, we specifically compare features related to the use case considered in this work. Method [11] is processed post-hoc, whereas methods [12; 13; 14; 15] have no defined behavior of how to use the calculated importance values to compress unimportant data. Out of the methods used for comparison, only related work [10; 16; 17] explore using the data importance to prioritize compression or reduction of unimportant data. However, in contrast to our work, none of the methods support lossless compression or simultaneously using multiple compression and reduction methods. In addition, there is no defined behavior of how to use the methods for in-transit co-processing.