Sensor networks, which consist of sensor nodes each capable of sensing environment and transmitting data, have lots of applications in battlefield surveillance, environmental monitoring, industrial diagnostics, etc. Coverage which is one of the most important performance metrics for sensor networks reflects how well a sensor field is monitored. Individual sensor coverage models are dependent on the sensing functions of different types of sensors, while network-wide sensing coverage is a collective performance measure for geographically distributed sensor nodes. This article surveys research progress made to address various coverage problems in sensor networks. We first provide discussions on sensor coverage models and design issues. The coverage problems in sensor networks can be classified into three categories according to the subject to be covered. We state the basic coverage problems in each category, and review representative solution approaches in the literature. We also provide comments and discussions on some extensions and variants of these basic coverage problems.

Coverage problems in sensor networks: A survey

Maximizing the lifetime of wireless sensor networks (WSNs) is a challenging problem. Although some methods exist to address the problem in homogeneous WSNs, research on this problem in heterogeneous WSNs have progressed at a slow pace. Inspired by the promising performance of ant colony optimization (ACO) to solve combinatorial problems, this paper proposes an ACO-based approach that can maximize the lifetime of heterogeneous WSNs. The methodology is based on finding the maximum number of disjoint connected covers that satisfy both sensing coverage and network connectivity. A construction graph is designed with each vertex denoting the assignment of a device in a subset. Based on pheromone and heuristic information, the ants seek an optimal path on the construction graph to maximize the number of connected covers. The pheromone serves as a metaphor for the search experiences in building connected covers. The heuristic information is used to reflect the desirability of device assignments. A local search procedure is designed to further improve the search efficiency. The proposed approach has been applied to a variety of heterogeneous WSNs. The results show that the approach is effective and efficient in finding high-quality solutions for maximizing the lifetime of heterogeneous WSNs.

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An Ant Colony Optimization Approach for Maximizing the Lifetime of Heterogeneous Wireless Sensor Networks

Definitions and basic properties of the Voronoi diagram generalizations of the Voronoi diagram algorithms for computing Voronoi diagrams poisson Voronoi diagrams spatial interpolation models of spatial processes point pattern analysis locational optimization through Voronoi diagrams.

Spatial tessellations. Concepts and Applications of Voronoi diagrams

Given a selfadjoint, elliptic operator L, one would like to know how the spectrum changes as the spatial domain Ω ⊂ ℝ n is deformed. For a family of domains {Ω t } t∈[a, b] we prove that the Morse index of L on Ω a differs from the Morse index of L on Ω b by the Maslov index of a path of Lagrangian subspaces on the boundary of Ω. This is particularly useful when Ω a is a domain for which the Morse index is known, e.g. a region with very small volume. Then the Maslov index computes the difference of Morse indices for the “original” problem (on Ω b ) and the “simplified” problem (on Ω a ). This generalizes previous multi-dimensional Morse index theorems that were only available on star-shaped domains or for Dirichlet boundary conditions. We also discuss how one can compute the Maslov index using crossing forms, and present some applications to the spectral theory of Dirichlet and Neumann boundary value problems.

A Morse Index Theorem for Elliptic Operators on Bounded Domains

We consider the Steklov eigenvalues of the Laplace operator as limiting Neumann eigenvalues in a problem of boundary mass concentration. We discuss the asymptotic behavior of the Neumann eigenvalues in a ball and we deduce that the Steklov eigenvalues minimize the Neumann eigenvalues. Moreover, we study the dependence of the eigenvalues of the Steklov problem upon perturbation of the mass density and show that the Steklov eigenvalues violates a maximum principle in spectral optimization problems.

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Viewing the Steklov eigenvalues of the Laplace operator as critical Neumann eigenvalues

One of the most serious concerns for wireless sensor networks (WSN) is energy. To obtain long lifetime, one potential method is deploying redundant sensors in the WSN and let each sensor switch its state between ACTIVE and OFF. At the same time, the WSN should meet various requirements of quality of service (QoS). This paper focuses on two important measurements of OoS: sensing coverage and network connectivity. Existing researches have provided many algorithms to schedule the nodes' states for coverage preserving, including location-free ones. Our work differs from existing location-free algorithms in several key ways: (1). We propose a novel principle on coverage preserving that is suitable for location-free schemes; (2). Following the principle, a distributed, localized and location-free node scheduling algorithm, Stand Guard Algorithm (StanGA), is proposed for treating coverage and connectivity in a unified scheme. Under certain conditions, StanGA can guarantee network connectivity and any degree of sensing coverage. Simulation results show that StanGA is scalable and robust, and also show that StanGA outperforms existing location-free algorithms even when only coverage issue is considered.

Dianfei Han

Papers

A Location-free Algorithm of Energy-Efficient Connected Coverage for High Density Wireless Sensor Networks