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<p>Accurate clustering of IoT devices is a promising challenge. We have observed that a few studies have been performed to address this challenge. However, they are expensive or do not shape accurate clustering. To fill this gap, in this study, we first solve a geometric version of a big challenge in pure mathematics: the NP-hard “Almost <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="41598_2025_88932_Article_IEq1.gif" Format="GIF" Height="15" Rendition="HTML" Resolution="72" Type="Linedraw" Width="67" /> </InlineMediaObject> <EquationSource Format="TEX">\(2-SAT\)</EquationSource> </InlineEquation>” problem. Then, we solve it in a polynomial time. To clarify the concept, we present it as the “Two Disjoint Convex Hulls” challenge. We solve this challenge using two algorithms: the first is “Naive” and the second is faster than the “Naive” one can solve it in polynomial order, <InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="41598_2025_88932_Article_IEq2.gif" Format="GIF" Height="20" Rendition="HTML" Resolution="72" Type="Linedraw" Width="44" /> </InlineMediaObject> <EquationSource Format="TEX">\(O(n^2)\)</EquationSource> </InlineEquation>. In addition to providing a mathematical proof of our solution, we demonstrate its superior performance within an IoT industrial ecosystem.</p>

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Reducing the clustering challenge in the IoT using two disjoint convex hulls

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年5月17日

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  • Huxiong Li,
  • Bahram Sadeghi Bigham,
  • Mehdi Gheisari,
  • Aminreza Karamoozian,
  • Panjun Sun,
  • Yi Wan

摘要

Accurate clustering of IoT devices is a promising challenge. We have observed that a few studies have been performed to address this challenge. However, they are expensive or do not shape accurate clustering. To fill this gap, in this study, we first solve a geometric version of a big challenge in pure mathematics: the NP-hard “Almost \(2-SAT\) ” problem. Then, we solve it in a polynomial time. To clarify the concept, we present it as the “Two Disjoint Convex Hulls” challenge. We solve this challenge using two algorithms: the first is “Naive” and the second is faster than the “Naive” one can solve it in polynomial order, \(O(n^2)\) . In addition to providing a mathematical proof of our solution, we demonstrate its superior performance within an IoT industrial ecosystem.