The Quest for Optimal Sorting Networks: Efficient Generation of Two-Layer Prefixes

Previous work identifying depth-optimal n-channel sorting networks for 9 ≤ n ≤ 16 is based on exploiting symmetries of the first two layers. However, the naive generate-and-test approach typically applied does not scale. This paper revisits the problem of generating two-layer prefixes modulo symmetr...

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Bibliographic Details
Published in:2014 16th International Symposium on Symbolic and Numeric Algorithms for Scientific Computing pp. 359 - 366
Main Authors: Codish, Michael, Cruz-Filipe, Luis, Schneider-Kamp, Peter
Format: Conference Proceeding
Language:English
Published: IEEE 01.09.2014
Subjects:
Computer science
Educational institutions
Joining processes
Runtime
Sorting
Syntactics
ISBN:9781479984473, 1479984477
Online Access:Get full text
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Summary:Previous work identifying depth-optimal n-channel sorting networks for 9 ≤ n ≤ 16 is based on exploiting symmetries of the first two layers. However, the naive generate-and-test approach typically applied does not scale. This paper revisits the problem of generating two-layer prefixes modulo symmetries. An improved notion of symmetry is provided and a novel technique based on regular languages and graph isomorphism is shown to generate the set of non-symmetric representations. An empirical evaluation demonstrates that the new method outperforms the generate-and-test approach by orders of magnitude and easily scales until n = 40.
ISBN:9781479984473
1479984477
DOI:10.1109/SYNASC.2014.55