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Exact Lower Bounds for the Number of Comparisons in Selection

Authors Josua Dörrer , Konrad Gendle , Johanna Betz , Julius von Smercek , Andreas Steding, Florian Stober

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Subject Classification

ACM Subject Classification
  • Theory of computation → Sorting and searching
  • Mathematics of computing → Combinatorial algorithms
Keywords
  • selection
  • lower bounds
  • exhaustive computer search

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Abstract

Selection is the problem of finding the i-th smallest element among n elements. We apply computer search to find optimal algorithms for small instances of the selection problem. Using new algorithmic ideas, we establish tighter lower bounds for the number of comparisons required, denoted as V_i(n). Our results include optimal algorithms for n up to 15 and arbitrary i, and for n = 16 when i ≤ 6. We determine the precise values V₇(14) = 25, V₆(15) = V₇(15) = 26, and V₈(15) = 27, where previously, only a range was known.

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Josua Dörrer, Konrad Gendle, Johanna Betz, Julius von Smercek, Andreas Steding, and Florian Stober. Exact Lower Bounds for the Number of Comparisons in Selection. In 23rd International Symposium on Experimental Algorithms (SEA 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 338, pp. 16:1-16:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025) https://doi.org/10.4230/LIPIcs.SEA.2025.16

Author Details

Josua Dörrer
  • University of Stuttgart, Germany
Konrad Gendle
  • University of Stuttgart, Germany
Johanna Betz
  • University of Stuttgart, Germany
Julius von Smercek
  • University of Stuttgart, Germany
Andreas Steding
  • University of Stuttgart, Germany
Florian Stober
  • University of Stuttgart, Germany

Supplementary Materials

References

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    Software Heritage Logo archived version
    full metadata available at: https://doi.org/10.4230/artifacts.23788
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