A survey of submodular maximization under uniform and partition matroids, reviewing known greedy, continuous, and distributed algorithms with no new results.
Providing Meaningful Data Summarizations Using Exemplar-based Clustering in Industry 4.0
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abstract
Data summarizations are a valuable tool to derive knowledge from large data streams and have proven their usefulness in a great number of applications. Summaries can be found by optimizing submodular functions. These functions map subsets of data to real values, which indicate their "representativeness" and which should be maximized to find a diverse summary of the underlying data. In this paper, we studied Exemplar-based clustering as a submodular function and provide a GPU algorithm to cope with its high computational complexity. We show, that our GPU implementation provides speedups of up to 72x using single-precision and up to 452x using half-precision computation compared to conventional CPU algorithms. We also show, that the GPU algorithm not only provides remarkable runtime benefits with workstation-grade GPUs but also with low-power embedded computation units for which speedups of up to 35x are possible. Furthermore, we apply our algorithm to real-world data from injection molding manufacturing processes and discuss how found summaries help with steering this specific process to cut costs and reduce the manufacturing of bad parts. Beyond pure speedup considerations, we show, that our approach can provide summaries within reasonable time frames for this kind of industrial, real-world data.
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Submodular Maximization Subject to Uniform and Partition Matroids: From Theory to Practical Applications and Distributed Solutions
A survey of submodular maximization under uniform and partition matroids, reviewing known greedy, continuous, and distributed algorithms with no new results.