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Updated: Jul 6, 2026

Large Scale Energy Efficient Sensor Network Routing Using a Quantum Processor Unit
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Large Scale Energy Efficient Sensor Network Routing Using a Quantum Processor Unit

Published on: September 8, 2023

Minimum Vertex Cut with Reachable Set (MVCRS) Problem for Suppressing Botnet Propagation in IoT Networks: Complexity

Shingo Yamaguchi1

  • 1Graduate School of Sciences and Technology for Innovation, Yamaguchi University, Ube 755-8611, Japan.

Sensors (Basel, Switzerland)
|May 4, 2026
PubMed
Summary

This study introduces the Minimum Vertex Cut with Reachable Set (MVCRS) problem to combat botnet spread in IoT networks. An efficient algorithm guarantees optimal suppression, outperforming traditional methods.

Keywords:
IoT securitybotnet containmentcomputational complexitydiffusion controlmaximum flow minimum cut theoremnetwork resiliencereachable set optimization

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Last Updated: Jul 6, 2026

Large Scale Energy Efficient Sensor Network Routing Using a Quantum Processor Unit
05:30

Large Scale Energy Efficient Sensor Network Routing Using a Quantum Processor Unit

Published on: September 8, 2023

Area of Science:

  • Cybersecurity
  • Network Science
  • Optimization Theory

Background:

  • Botnet propagation poses a significant threat to networked systems, particularly the Internet of Things (IoT).
  • Effective mitigation strategies require optimal resource allocation for damage control.
  • Existing heuristic approaches often fail to identify critical network vulnerabilities.

Purpose of the Study:

  • To formulate the Minimum Vertex Cut with Reachable Set (MVCRS) problem as an optimization framework.
  • To analyze the computational complexity and develop algorithmic solutions for MVCRS.
  • To establish a theoretical baseline for optimal resource allocation in cybersecurity for botnet suppression.

Main Methods:

  • Defining the MVCRS problem to minimize resource deployment cost and propagation scope.
  • Demonstrating the NP-completeness of the constrained MVCRS problem.
  • Reducing the fundamental trade-off optimization model to the maximum flow-minimum cut problem for polynomial-time solvability.

Main Results:

  • The fundamental MVCRS optimization model is solvable in polynomial time.
  • Conventional heuristics, like degree-based greedy algorithms, exhibit significant optimality gaps (up to 72.6%) in community-structured networks.
  • The proposed exact algorithm achieves optimal minimum cost (0% gap) with high stability and scales efficiently for large IoT networks.

Conclusions:

  • The MVCRS optimization framework provides a theoretically sound and practically efficient foundation for botnet suppression.
  • The exact algorithm offers a reliable solution for optimal resource allocation in complex, real-world networked systems.
  • This work highlights the limitations of heuristics and the importance of exact algorithms for critical cybersecurity challenges.