The <i>Search-o-Sort</i> Theory
In the modern era of informatics, where data are very important, efficient management of data is necessary and critical. Two of the most important data management techniques are searching and data ordering (technically sorting). Traditional sorting algorithms work in quadratic time <inline-formul...
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| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
| Published: |
MDPI AG
2025-05-01
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| Series: | AppliedMath |
| Subjects: | |
| Online Access: | https://www.mdpi.com/2673-9909/5/2/64 |
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| Summary: | In the modern era of informatics, where data are very important, efficient management of data is necessary and critical. Two of the most important data management techniques are searching and data ordering (technically sorting). Traditional sorting algorithms work in quadratic time <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mfenced separators="" open="(" close=")"><mi mathvariant="script">O</mi><mfenced separators="" open="(" close=")"><msup><mi>x</mi><mn>2</mn></msup></mfenced></mfenced></semantics></math></inline-formula>, and in the optimized cases, they take linearithmic time <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mfenced separators="" open="(" close=")"><mi mathvariant="script">O</mi><mfenced separators="" open="(" close=")"><mi>x</mi><mspace width="0.166667em"></mspace><mo>·</mo><mspace width="0.166667em"></mspace><mi>log</mi><mi>x</mi></mfenced></mfenced></semantics></math></inline-formula>, with no existing method surpass this lower bound, given arbitrary data, i.e., ordering a list of cardinality <i>x</i> in <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mfenced separators="" open="(" close=")"><mi mathvariant="script">O</mi><mfenced separators="" open="(" close=")"><mi>x</mi><mspace width="0.166667em"></mspace><mo>·</mo><mspace width="0.166667em"></mspace><mi>log</mi><mi>x</mi></mfenced><mo>−</mo><mi>ϵ</mi><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow></mfenced><mspace width="4pt"></mspace><mo>∀</mo><mi>ϵ</mi><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow><mo>></mo><mn>0</mn></mrow></semantics></math></inline-formula>. This research proposes <i>Search-o-Sort</i>, which reinterprets sorting in terms of searching, thereby offering a new framework for ordering arbitrary data. The framework is applied to classical search algorithms,–Linear Search, Binary Search (in general, <i>k</i>-ary Search), and extended to more optimized methods such as Interpolation and Jump Search. The analysis suggests theoretical pathways to reduce the computational complexity of sorting algorithms, thus enabling algorithmic development based on the proposed viewpoint. |
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| ISSN: | 2673-9909 |