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<p>Optimization is the need of the hour! In the ever-evolving world of informatics, algorithmic optimization, which employs strategies to reduce resource usage and improve efficiency or throughput, is important. This research aims to optimize the generic version of partition-based retrieval algorithms, <i>k</i>-ary Search, by choosing a value of partition parameter (<InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="41870_2025_2546_Article_IEq1.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="42" /> </InlineMediaObject> <EquationSource Format="TEX">\(k&gt;1\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>k</mi> <mo>&gt;</mo> <mn>1</mn> </mrow> </math></EquationSource> </InlineEquation>) that minimizes the temporal complexity. It is established mathematically, and by graphical simulation in this research that, for <InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="41870_2025_2546_Article_IEq2.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="41" /> </InlineMediaObject> <EquationSource Format="TEX">\(k=2\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>k</mi> <mo>=</mo> <mn>2</mn> </mrow> </math></EquationSource> </InlineEquation>, the computational complexity demands the least. Several existing pieces of literature are likely to be supplemented following the dissemination of this research, for instance, the minimal computational complexity of sorting algorithms, self-adjusting networks, etc.</p>

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k-Optima: Finding the Optimal Partition Parameter for k-ary Search

  • 期刊论文

  • 发表日期：

    2025年5月18日

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  • Anurag Dutta,
  • K. Lakshmanan

摘要

Optimization is the need of the hour! In the ever-evolving world of informatics, algorithmic optimization, which employs strategies to reduce resource usage and improve efficiency or throughput, is important. This research aims to optimize the generic version of partition-based retrieval algorithms, k-ary Search, by choosing a value of partition parameter ( \(k>1\) k > 1 ) that minimizes the temporal complexity. It is established mathematically, and by graphical simulation in this research that, for \(k=2\) k = 2 , the computational complexity demands the least. Several existing pieces of literature are likely to be supplemented following the dissemination of this research, for instance, the minimal computational complexity of sorting algorithms, self-adjusting networks, etc.