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

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 [Formula: see text]" 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, [Formula: see text]. In addition to providing a mathematical proof of our solution, we demonstrate its superior performance within an IoT industrial ecosystem.

Publication Details

Journal
Figshare
Published
2025-01-01
DOI
https://doi.org/10.6084/m9.figshare.29888972.v1
Primary Topic
Advanced Clustering Algorithms Research
Type
article
Field-Weighted Citation Impact
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article

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

Figshare
Advanced Clustering Algorithms Research
article

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

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Abstract

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 [Formula: see text]" 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, [Formula: see text]. In addition to providing a mathematical proof of our solution, we demonstrate its superior performance within an IoT industrial ecosystem.

Figshare
Openalex Percentile: Top 77%
Advanced Clustering Algorithms Research
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