On sublattices of the hexagonal lattice
Discrete Mathematics
Set k-cover algorithms for energy efficient monitoring in wireless sensor networks
Proceedings of the 3rd international symposium on Information processing in sensor networks
Uncertainty-aware and coverage-oriented deployment for sensor networks
Journal of Parallel and Distributed Computing
Deploying wireless sensors to achieve both coverage and connectivity
Proceedings of the 7th ACM international symposium on Mobile ad hoc networking and computing
Connected sensor cover: self-organization of sensor networks for efficient query execution
IEEE/ACM Transactions on Networking (TON)
Minimum-cost coverage of point sets by disks
Proceedings of the twenty-second annual symposium on Computational geometry
The coverage problem in a wireless sensor network
Mobile Networks and Applications
Improved approximation algorithms for connected sensor cover
Wireless Networks
Bounds on coverage and target detection capabilities for models of networks of mobile sensors
ACM Transactions on Sensor Networks (TOSN)
Decomposition of multiple coverings into many parts
SCG '07 Proceedings of the twenty-third annual symposium on Computational geometry
Power management in energy harvesting sensor networks
ACM Transactions on Embedded Computing Systems (TECS) - Special Section LCTES'05
Snap and Spread: A Self-deployment Algorithm for Mobile Sensor Networks
DCOSS '08 Proceedings of the 4th IEEE international conference on Distributed Computing in Sensor Systems
Distributed Deployment Schemes for Mobile Wireless Sensor Networks to Ensure Multilevel Coverage
IEEE Transactions on Parallel and Distributed Systems
Cheap or Flexible Sensor Coverage
DCOSS '09 Proceedings of the 5th IEEE International Conference on Distributed Computing in Sensor Systems
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Positioning disk-shaped sensors to optimize certain coverage parameters is a fundamental problem in ad hoc sensor networks. The hexagon lattice arrangement is known to be optimally efficient in the plane, even though 20.9% of the area is unnecessarily covered twice, however, the arrangement is very rigid—any movement of a sensor from its designated grid position (due to, e.g., placement error or obstacle avoidance) leaves some region uncovered, as would the failure of any one sensor. In this article, we consider how to arrange sensors in order to guarantee multiple coverage, that is, k-coverage for some value k 1. A naive approach is to superimpose multiple hexagon lattices, but for robustness reasons, we may wish to space sensors evenly apart. We present two arrangement methods for k-coverage: (1) optimizing a Riesz energy function in order to evenly distribute nodes, and (2) simply shrinking the hexagon lattice and making it denser. The first method often approximates the second, and so we focus on the latter. We show that a density increase tantamount to k copies of the lattice can yield k′-coverage, for k′ k (e.g., k = 11, k′ = 12 and k = 21, k′ = 24), by exploiting the double-coverage regions. Our examples' savings provably converge in the limit to the ≈ 20.9% maximum. We also provide analogous results for the square lattice and its ≈ 57% inefficiency (e.g., k = 3, k′ = 4 and k=5, k′ = 7) and show that for multi-coverage for some values of k′, the square lattice can actually be more efficient than the hexagon lattice. We also explore other benefits of shrinking the lattice: Doing so allows all sensors to move about their intended positions independently while nonetheless guaranteeing full coverage and can also allow us to tolerate probabilistic sensor failure when providing 1-coverage or k-coverage. We conclude by construing the shrinking factor as a budget to be divided among these three benefits.