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This study addresses the mobile sensor deployment problem for maximizing weighted points covered on a line. It presents optimal and approximation algorithms for sensors with identical and varying velocities, proving NP-hardness for the latter.

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Area of Science:

  • Wireless Sensor Networks (WSNs)
  • Computational Geometry
  • Algorithm Design

Background:

  • Mobile sensor deployment for periodic monitoring (sweep coverage) is crucial for applications like environmental monitoring.
  • The point sweep coverage problem is NP-hard for sensors on Eulerian graphs, even with uniform velocity.
  • Existing research often assumes uniform sensor speeds, limiting applicability.

Purpose of the Study:

  • To investigate the problem of maximizing the total weight of points of interest (PoIs) on a line covered by mobile sensors with potentially different velocities.
  • To establish the computational complexity of this problem and develop efficient algorithmic solutions.
  • To provide both optimal and approximation algorithms for various sensor velocity scenarios.

Main Methods:

  • Proving the NP-hardness of the weighted point sweep coverage problem for mobile sensors with distinct velocities.
  • Developing an optimal algorithm for sensors with the same velocity, achieving O(MN) time complexity.
  • Designing polynomial-time approximation algorithms for sensors with constant or arbitrary velocities, offering trade-offs between time and approximation ratio.

Main Results:

  • The problem is proven NP-hard for sensors with different velocities.
  • An O(MN) optimal algorithm is presented for sensors with identical velocities.
  • Approximation algorithms with ratios of 12, 12α, and 12(1-1/e) are developed for different velocity scenarios.

Conclusions:

  • The study provides a comprehensive analysis of the weighted point sweep coverage problem for mobile sensors on a line.
  • Efficient algorithms, including optimal and approximation solutions, are presented for various sensor velocity constraints.
  • The findings contribute to the practical deployment of mobile sensors in real-world monitoring applications.