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June 2013 Distributional convergence for the number of symbol comparisons used by QuickSelect
James Allen Fill, Takehiko Nakama
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Adv. in Appl. Probab. 45(2): 425-450 (June 2013). DOI: 10.1239/aap/1370870125


When the search algorithm QuickSelect compares keys during its execution in order to find a key of target rank, it must operate on the keys' representations or internal structures, which were ignored by the previous studies that quantified the execution cost for the algorithm in terms of the number of required key comparisons. In this paper we analyze running costs for the algorithm that take into account not only the number of key comparisons, but also the cost of each key comparison. We suppose that keys are represented as sequences of symbols generated by various probabilistic sources and that QuickSelect operates on individual symbols in order to find the target key. We identify limiting distributions for the costs, and derive integral and series expressions for the expectations of the limiting distributions. These expressions are used to recapture previously obtained results on the number of key comparisons required by the algorithm.


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James Allen Fill. Takehiko Nakama. "Distributional convergence for the number of symbol comparisons used by QuickSelect." Adv. in Appl. Probab. 45 (2) 425 - 450, June 2013.


Published: June 2013
First available in Project Euclid: 10 June 2013

zbMATH: 1278.68354
MathSciNet: MR3102458
Digital Object Identifier: 10.1239/aap/1370870125

Primary: 60F25
Secondary: 68W40

Rights: Copyright © 2013 Applied Probability Trust


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Vol.45 • No. 2 • June 2013
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