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

Area of Science:

• Computer Science
• Computational Geometry
• Network Engineering

Background:

• Accurate clustering of Internet of Things (IoT) devices is a significant challenge.
• Existing solutions for IoT device clustering are often expensive or lack precision.
• There is a need for efficient and accurate methods for IoT device clustering.

Purpose of the Study:

• To address the gap in accurate and cost-effective IoT device clustering.
• To solve a geometric version of the NP-hard "Almost [Formula: see text]" problem in polynomial time.
• To introduce and solve the "Two Disjoint Convex Hulls" challenge for improved IoT device clustering.

Main Methods:

• Solving the NP-hard "Almost [Formula: see text]" problem using geometric approaches.
• Developing two algorithms: a "Naive" algorithm and a faster polynomial-time algorithm for the "Two Disjoint Convex Hulls" challenge.
• Providing mathematical proofs for the proposed algorithms.

Main Results:

• The "Two Disjoint Convex Hulls" challenge is solved in polynomial time.
• The developed algorithms demonstrate superior performance compared to existing methods.
• The solution is validated within an industrial Internet of Things (IoT) ecosystem.

Conclusions:

• The proposed algorithms offer an efficient and accurate solution for IoT device clustering.
• This work contributes a novel mathematical approach to a practical IoT challenge.
• The findings have implications for optimizing IoT industrial ecosystems.