Counting Zeros in Random Walks on the Integers and Analysis of Optimal Dual-Pivot Quicksort

Martin Aumüller, Martin Dietzfelbinger, Clemens Heuberger, Daniel Krenn, Helmut Prodinger

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Abstract

We present an average case analysis of two variants of dual-pivot quicksort, one with a non-algorithmic
comparison-optimal partitioning strategy, the other with a closely related algorithmic strategy. For both
we calculate the expected number of comparisons exactly as well as asymptotically, in particular, we
provide exact expressions for the linear, logarithmic, and constant terms. An essential step is the analysis
of zeros of lattice paths in a certain probability model. Along the way a combinatorial identity is proven.
OriginalsprogEngelsk
TitelProceedings of the 27th Conference on Probabilistic, Combinatorial and Asymptotic Methods for the Analysis of Algorithms
Antal sider13
ForlagJagiellonian University in Krakow
Publikationsdato4 jul. 2016
StatusUdgivet - 4 jul. 2016
BegivenhedInternational Conference on Probabilistic, Combinatorial and Asymptotic Methods for the Analysis of Algorithms - Jagiellonian University, Kraków, Polen
Varighed: 4 jul. 20167 jul. 2016
Konferencens nummer: 27
http://www.aofa2016.meetings.pl/

Konference

KonferenceInternational Conference on Probabilistic, Combinatorial and Asymptotic Methods for the Analysis of Algorithms
Nummer27
LokationJagiellonian University
Land/OmrådePolen
ByKraków
Periode04/07/201607/07/2016
Internetadresse

Emneord

  • Dual-pivot quicksort
  • Average case analysis
  • Comparison-optimal partitioning
  • Algorithmic strategy
  • Lattice paths analysis

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