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Algorithmica

, Volume 81, Issue 2, pp 796–827 | Cite as

Sorting by Swaps with Noisy Comparisons

  • Tomáš Gavenčiak
  • Barbara Geissmann
  • Johannes LenglerEmail author
Article
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Part of the following topical collections:
  1. Special Issue on Theory of Genetic and Evolutionary Computation

Abstract

We study sorting of permutations by random swaps if each comparison gives the wrong result with some fixed probability \(p<1/2\). We use this process as prototype for the behaviour of randomized, comparison-based optimization heuristics in the presence of noisy comparisons. As quality measure, we compute the expected fitness of the stationary distribution. To measure the runtime, we compute the minimal number of steps after which the average fitness approximates the expected fitness of the stationary distribution. We study the process where in each round a random pair of elements at distance at most r are compared. We give theoretical results for the extreme cases \(r=1\) and \(r=n\), and experimental results for the intermediate cases. We find a trade-off between faster convergence (for large r) and better quality of the solution after convergence (for small r).

Keywords

Sorting Random swaps Evolutionary algorithms Comparison-based Noise Optimization heuristics 
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Notes

Acknowledgements

We would like to thank all the anonymous reviewers for their careful and attentive reading, as well as their numerous helpful comments to improve this paper. Tomáš Gavenčiak was supported by the Czech Science Foundation (GAČR) Project 17-10090Y “Network optimization”. Barbara Geissmann was supported by the Swiss National Science Foundation (SNSF), Project Number 200021_165524.

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© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of Applied MathematicsCharles UniversityPragueCzech Republic
  2. 2.Department of Computer Science, FEECTUPragueCzech Republic
  3. 3.Department of Computer ScienceETH ZurichZurichSwitzerland

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