Abstract
We present new parallel sorting networks for \(17\) to \(20\) inputs. For \(17, 19,\) and \(20\) inputs these new networks are faster (i.e., they require fewer computation steps) than the previously known best networks. Therefore, we improve upon the known upper bounds for minimal depth sorting networks on \(17, 19,\) and \(20\) channels. Furthermore, we show that our sorting network for \(17\) inputs is optimal in the sense that no sorting network using less layers exists. This solves the main open problem of [D. Bundala & J. Závodný. Optimal sorting networks, Proc. LATA 2014].
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Acknowledgments
We would like to thank Michael Codish, Luís Cruz-Filipe, and Peter Schneider-Kamp for fruitful discussions on the subject and their valuable comments on an earlier draft of this article. Furthermore, we thank Dirk Nowotka for providing us with the computational resources to run our experiments. We thank Donald E. Knuth and the anonymous reviewers for their helpful comments on this paper.
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Ehlers, T., Müller, M. (2015). New Bounds on Optimal Sorting Networks. In: Beckmann, A., Mitrana, V., Soskova, M. (eds) Evolving Computability. CiE 2015. Lecture Notes in Computer Science(), vol 9136. Springer, Cham. https://doi.org/10.1007/978-3-319-20028-6_17
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DOI: https://doi.org/10.1007/978-3-319-20028-6_17
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