Coverage Protocols for Wireless Sensor Networks: Review and Future Directions

The coverage problem in wireless sensor networks (WSNs) can be generally defined as a measure of how effectively a network field is monitored by its sensor nodes. This problem has attracted a lot of interest over the years and as a result, many coverage protocols were proposed. In this survey, we first propose a taxonomy for classifying coverage protocols in WSNs. Then, we classify the coverage protocols into three categories (i.e. coverage aware deployment protocols, sleep scheduling protocols for flat networks, and cluster-based sleep scheduling protocols) based on the network stage where the coverage is optimized. For each category, relevant protocols are thoroughly reviewed and classified based on the adopted coverage techniques. Finally, we discuss open issues (and recommend future directions to resolve them) associated with the design of realistic coverage protocols. Issues such as realistic sensing models, realistic energy consumption models, realistic connectivity models and sensor localization are covered

Minimum-Weight Edge Discriminator in Hypergraphs

In this paper we introduce the concept of minimum-weight edge-discriminators in hypergraphs, and study its various properties. For a hypergraph $\mathcal H=(\mathcal V, \mathcal E)$, a function $\lambda: \mathcal V\rightarrow \mathbb Z^{+}\cup\{0\}$ is said to be an {\it edge-discriminator} on $\mathcal H$ if $\sum_{v\in E_i}{\lambda(v)}>0$, for all hyperedges $E_i\in \mathcal E$, and $\sum_{v\in E_i}{\lambda(v)}\ne \sum_{v\in E_j}{\lambda(v)}$, for every two distinct hyperedges $E_i, E_j \in \mathcal E$. An {\it optimal edge-discriminator} on $\mathcal H$, to be denoted by $\lambda_\mathcal H$, is an edge-discriminator on $\mathcal H$ satisfying $\sum_{v\in \mathcal V}\lambda_\mathcal H (v)=\min_\lambda\sum_{v\in \mathcal V}{\lambda(v)}$, where the minimum is taken over all edge-discriminators on $\mathcal H$. We prove that any hypergraph $\mathcal H=(\mathcal V, \mathcal E)$, with $|\mathcal E|=n$, satisfies $\sum_{v\in \mathcal V} \lambda_\mathcal H(v)\leq n(n+1)/2$, and equality holds if and only if the elements of $\mathcal E$ are mutually disjoint. For $r$-uniform hypergraphs $\mathcal H=(\mathcal V, \mathcal E)$, it follows from results on Sidon sequences that $\sum_{v\in \mathcal V}\lambda_{\mathcal H}(v)\leq |\mathcal V|^{r+1}+o(|\mathcal V|^{r+1})$, and the bound is attained up to a constant factor by the complete $r$-uniform hypergraph. Next, we construct optimal edge-discriminators for some special hypergraphs, which include paths, cycles, and complete $r$-partite hypergraphs. Finally, we show that no optimal edge-discriminator on any hypergraph $\mathcal H=(\mathcal V, \mathcal E)$, with $|\mathcal E|=n (\geq 3)$, satisfies $\sum_{v\in \mathcal V} \lambda_\mathcal H (v)=n(n+1)/2-1$, which, in turn, raises many other interesting combinatorial questions.Comment: 22 pages, 5 figure

Sparse Localization with a Mobile Beacon Based on LU Decomposition in Wireless Sensor Networks

Node localization is the core in wireless sensor network. It can be solved by powerful beacons, which are equipped with global positioning system devices to know their location information. In this article, we present a novel sparse localization approach with a mobile beacon based on LU decomposition. Our scheme firstly translates node localization problem into a 1-sparse vector recovery problem by establishing sparse localization model. Then, LU decomposition pre-processing is adopted to solve the problem that measurement matrix does not meet the re¬stricted isometry property. Later, the 1-sparse vector can be exactly recovered by compressive sensing. Finally, as the 1-sparse vector is approximate sparse, weighted Cen¬troid scheme is introduced to accurately locate the node. Simulation and analysis show that our scheme has better localization performance and lower requirement for the mobile beacon than MAP+GC, MAP-M, and MAP-M&N schemes. In addition, the obstacles and DOI have little effect on the novel scheme, and it has great localization performance under low SNR, thus, the scheme proposed is robust