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The NP-hard scheduling problem P||C_max encompasses a set of tasks with known execution time which must be mapped to a set of identical machines such that the overall completion time is minimized. In this work, we improve existing techniques for optimal P||C_max scheduling with a combination of new theoretical insights and careful practical engineering. Most importantly, we derive techniques to prune vast portions of the search space of branch-and-bound (BnB) approaches. We also propose improved upper and lower bounding techniques which can be combined with any approach to P||C_max. Moreover, we present new benchmarks for P||C_max, based on diverse application data, which can shed light on aspects which prior synthetic instances fail to capture. In an extensive evaluation, we observe that our pruning techniques reduce the number of explored nodes by 90$\times$ and running times by 12$\times$. Compared to a state-of-the-art ILP-based approach, our approach is preferable for short running time limits and for instances with large makespans.

With growing complexity and responsibility of automated driving functions in road traffic and growing scope of their operational design domains, there is increasing demand for covering significant parts of development, validation, and verification via virtual environments and simulation models. If, however, simulations are meant not only to augment real-world experiments, but to replace them, quantitative approaches are required that measure to what degree and under which preconditions simulation models adequately represent reality, and thus allow their usage for virtual testing of driving functions. Especially in research and development areas related to the safety impacts of the "open world", there is a significant shortage of real-world data to parametrize and/or validate simulations - especially with respect to the behavior of human traffic participants, whom automated vehicles will meet in mixed traffic. This paper presents the intermediate results of the German AVEAS research project (www.aveas.org) which aims at developing methods and metrics for the harmonized, systematic, and scalable acquisition of real-world data for virtual verification and validation of advanced driver assistance systems and automated driving, and establishing an online database following the FAIR principles., Comment: 6 pages, 5 figures, 2 tables

Previous efforts on making Satisfiability (SAT) solving fit for high performance computing (HPC) have lead to super-linear speedups on particular formulae, but for most inputs cannot make efficient use of a large number of processors. Moreover, long latencies (minutes to days) of job scheduling make large-scale SAT solving on demand impractical for most applications. We address both issues with Mallob, a framework for job scheduling in the context of SAT solving which exploits malleability, i.e., the ability to add or remove processing power from a job during its computation. Mallob includes a massively parallel, distributed, and malleable SAT solving engine based on Hordesat with a more succinct and communication-efficient approach to clause sharing and numerous further improvements over its precursor. For example, Mallob on 640 cores outperforms an updated and improved configuration of Hordesat on 2560 cores. Moreover, Mallob can also solve many formulae in parallel while dynamically adapting the assigned resources, and jobs arriving in the system are usually initiated within a fraction of a second., Comment: This preprint has not undergone peer review or any post-submission improvements or corrections. The Version of Record of this contribution is published in the proceedings of the International Conference on Theory and Applications of Satisfiability Testing 2021 (pp. 518-534), Springer, Cham, and is available online at https://doi.org/10.1007/978-3-030-80223-3_35

We propose an exact algorithm for solving the longest simple path problem between two given vertices in undirected weighted graphs. By using graph partitioning and dynamic programming, we obtain an algorithm that is significantly faster than other state-of-the-art methods. This enables us to solve instances that were previously unsolved and solve hard instances significantly faster. Lastly, we present a scalable parallelization which yields the first efficient parallel algorithm for the problem., Comment: arXiv admin note: substantial text overlap with arXiv:1702.04170