Abstract
The non-dominated sorting algorithm by Jensen, generalized by Fortin et al to handle the cases of equal objective values, has the running time complexity of O(N logK − 1 N) in the general case. Here N is the number of points, K is the number of objectives and K is thought to be a constant when N varies. However, the complexity was not proven to be the same in the worst case.
A slightly modified version of the algorithm is presented, for which it is proven that its worst-case running time complexity is O(N logK − 1 N).
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References
Source code for the implementation (a part of this paper), https://github.com/mbuzdalov/papers/tree/master/2014-ppsn-jensen-fortin
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Buzdalov, M., Shalyto, A. (2014). A Provably Asymptotically Fast Version of the Generalized Jensen Algorithm for Non-dominated Sorting. In: Bartz-Beielstein, T., Branke, J., Filipič, B., Smith, J. (eds) Parallel Problem Solving from Nature – PPSN XIII. PPSN 2014. Lecture Notes in Computer Science, vol 8672. Springer, Cham. https://doi.org/10.1007/978-3-319-10762-2_52
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DOI: https://doi.org/10.1007/978-3-319-10762-2_52
Publisher Name: Springer, Cham
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