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Particle advection is the approach for the extraction of integral curves from vector fields. Efficient parallelization of particle advection is a challenging task due to the problem of load imbalance, in which processes are assigned unequal workloads, causing some of them to idle as the others are performing computing. Various approaches to load balancing exist, yet they all involve trade-offs such as increased inter-process communication, or the need for central control structures. In this work, we present two local load balancing methods for particle advection based on the family of diffusive load balancing. Each process has access to the blocks of its neighboring processes, which enables dynamic sharing of the particles based on a metric defined by the workload of the neighborhood. The approaches are assessed in terms of strong and weak scaling as well as load imbalance. We show that the methods reduce the total run-time of advection and are promising with regard to scaling as they operate locally on isolated process neighborhoods.

Tracking the temporal evolution of features in time-varying data is a key method in visualization. For typical feature definitions, such as vortices, objects are sparsely distributed over the data domain. In this paper, we present a novel approach for tracking both sparse and space-filling features. While the former comprise only a small fraction of the domain, the latter form a set of objects whose union covers the domain entirely while the individual objects are mutually disjunct. Our approach determines the assignment of features between two successive time-steps by solving two graph optimization problems. It first resolves one-to-one assignments of features by computing a maximum-weight, maximum-cardinality matching on a weighted bi-partite graph. Second, our algorithm detects events by creating a graph of potentially conflicting event explanations and finding a weighted, independent set in it. We demonstrate our method's effectiveness on synthetic and simulation data sets, the former of which enables quantitative evaluation because of the availability of ground-truth information. Here, our method performs on par or better than a well-established reference algorithm. In addition, manual visual inspection by our collaborators confirm the results' plausibility for simulation data.

Tracking the temporal evolution of features in time-varying data remains a combinatorially challenging problem. A recent method models event detection as a maximum-weight independent set problem on a graph representation of all possible explanations [35]. However, optimally solving this problem is NP-hard in the general case. Following the approach by Schnorr et al., we propose a new algorithm for event detection. Our algorithm exploits the modelspecific structure of the independent set problem. Specifically, we show how to traverse potential explanations in such a way that a greedy assignment provides reliably good results. We demonstrate the effectiveness of our approach on synthetic and simulation data sets, the former of which include ground-truth tracking information which enable a quantitative evaluation. Our results are within 1% of the theoretical optimum and comparable to an approximate solution provided by a state-of-the-art optimization package. At the same time, our algorithm is significantly faster.

Feature tracking is a method of time-varying data analysis. Due to the complexity of the underlying problem, different feature tracking algorithms have different levels of correctness in certain use cases. However, there is no efficient way to evaluate their performance on simulation data since there is no ground-truth easily obtainable. Synthetic data is a way to ensure a minimum level of correctness, though there are limits to their expressiveness when comparing the results to simulation data. To close this gap, we calculate a synthetic data set and use its results to extract a hypothesis about the algorithm performance that we can apply to simulation data.

We present an approach for tracking space-filling features based on a two-step algorithm utilizing two graph optimization techniques. First, one-to-one assignments between successive time steps are found by a matching on a weighted, bi-partite graph. Second, events are detected by computing an independent set on potential event explanations. The main objective of this work is investigating options for formal evaluation of complex feature tracking algorithms in the absence of ground truth data.