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Extensions of Self-Improving Sorters

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Abstract

Ailon et al. (SIAM J Comput 40(2):350–375, 2011) proposed a self-improving sorter that tunes its performance to an unknown input distribution in a training phase. The input numbers \(x_1,x_2,\ldots ,x_n\) come from a product distribution, that is, each \(x_i\) is drawn independently from an arbitrary distribution \({{{\mathcal {D}}}}_i\). We study two relaxations of this requirement. The first extension models hidden classes in the input. We consider the case that numbers in the same class are governed by linear functions of the same hidden random parameter. The second extension considers a hidden mixture of product distributions.

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Notes

  1. There is a technical condition required of the input distribution to be explained in Sect. 2.

  2. The space usage according to the description in [10] is \(O(m\log m)\), but it can be improved to O(m) as mentioned in [7].

References

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Acknowledgements

We thank the anonymous reviewers for their valuable comments, suggesting a cleaner proof of Lemma 3.5, and alerting us to mistakes that we subsequently corrected.

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Authors and Affiliations

  1. Department of Computer Science and Engineering, HKUST, Clear Water Bay, Hong Kong

    Siu-Wing Cheng & Kai Jin

  2. Hangzhou, China

    Lie Yan

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  1. Siu-Wing Cheng
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  2. Kai Jin
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Correspondence to Siu-Wing Cheng.

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S.-W. Cheng: Supported by Research Grants Council, Hong Kong, China (Project No. 16200317). L. Yan: Part of the work was conducted while the author was at HKUST and supported by the Hong Kong Ph.D. Fellowship.

A preliminary version appeared in Proceedings of the International Symposium on Algorithms and Computation, 2018 [2].

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Cheng, SW., Jin, K. & Yan, L. Extensions of Self-Improving Sorters. Algorithmica 82, 88–106 (2020). https://doi.org/10.1007/s00453-019-00604-6

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