Analysis of Algorithms for Permutations Biased by Their Number of Records

Abstract : The topic of the article is the parametric study of the complexity of algorithms on arrays of pairwise distinct integers. We introduce a model that takes into account the non-uniformness of data, which we call the Ewens-like distribution of parameter θ for records on permutations: the weight θ r of a permutation depends on its number r of records. We show that this model is meaningful for the notion of presortedness, while still being mathematically tractable. Our results describe the expected value of several classical permutation statistics in this model, and give the expected running time of three algorithms: the Insertion Sort, and two variants of the Min-Max search.
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https://hal.archives-ouvertes.fr/hal-01838692
Contributor : Carine Pivoteau <>
Submitted on : Friday, July 13, 2018 - 3:16:14 PM
Last modification on : Wednesday, July 25, 2018 - 4:10:42 PM
Long-term archiving on : Monday, October 15, 2018 - 11:40:54 AM

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Nicolas Auger, Mathilde Bouvel, Cyril Nicaud, Carine Pivoteau. Analysis of Algorithms for Permutations Biased by Their Number of Records. 27th International Conference on Probabilistic, Combinatorial and Asymptotic Methods for the Analysis of Algorithm AOFA 2016, Jul 2016, Cracovie, Poland. ⟨hal-01838692⟩

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