We propose two novel algorithms for distributed and location-free boundary recognition in wireless sensor networks. Both approaches enable a node to decide autonomously whether it is a boundary node, based solely on connectivity information of a small neighborhood. This makes our algorithms highly applicable for dynamic networks where nodes can move or become inoperative. We compare our algorithms qualitatively and quantitatively with several previous approaches. In extensive simulations, we consider various models and scenarios. Although our algorithms use less information than most other approaches, they produce significantly better results. They are very robust against variations in node degree and do not rely on simplified assumptions of the communication model. Moreover, they are much easier to implement on real sensor nodes than most existing approaches.
use information about node positions, distances between nodes, or angular relationships to detect network boundaries and holes. Accordingly, these approaches are limited to situations where GPS devices or similar equipment are available. Unfortunately, in many realistic scenarios this is not the case. Examples for geometrical approaches are Fang @cite_15 , Martincic @cite_2 , and Deogun @cite_10 .
@cite_15 @cite_10 @cite_2
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It is often useful to know the geographic positions of nodes in a communications network, but adding GPS receivers or other sophisticated sensors to every node can be expensive. We present an algorithm that uses connectivity information who is within communications range of whom to derive the locations of the nodes in the network. The method can take advantage of additional information, such as estimated distances between neighbors or known positions for certain anchor nodes, if it is available. The algorithm is based on multidimensional scaling, a data analysis technique that takes O(n3) time for a network of n nodes. Through simulation studies, we demonstrate that the algorithm is more robust to measurement error than previous proposals, especially when nodes are positioned relatively uniformly throughout the plane. Furthermore, it can achieve comparable results using many fewer anchor nodes than previous methods, and even yields relative coordinates when no anchor nodes are available. We consider the problem of node positioning in ad hoc networks. We propose a distributed, infrastructure-free positioning algorithm that does not rely on GPS (Global Positioning System). Instead, the algorithm uses the distances between the nodes to build a relative coordinate system in which the node positions are computed in two dimensions. Despite the distance measurement errors and the motion of the nodes, the algorithm provides sufficient location information and accuracy to support basic network functions. Examples of applications where this algorithm can be used include Location Aided Routing [10] and Geodesic Packet Forwarding [2]. Another example are sensor networks, where mobility is less of a problem. The main contribution of this work is to define and compute relative positions of the nodes in an ad hoc network without using GPS. We further explain how the proposed approach can be applied to wide area ad hoc networks. Evolving networks of ad-hoc wireless sensing nodes rely heavily on the ability to establish position information. The algorithms presented herein rely on range measurements between pairs of nodes and the a priori coordinates of sparsely located anchor nodes. Clusters of nodes surrounding anchor nodes cooperatively establish confident position estimates through assumptions, checks, and iterative refinements. Once established, these positions are propagated to more distant nodes, allowing the entire network to create an accurate map of itself. Major obstacles include overcoming inaccuracies in range measurements as great as spl plusmn 50 , as well as the development of initial guesses for node locations in clusters with few or no anchor nodes. Solutions to these problems are presented and discussed, using position error as the primary metric. Algorithms are compared according to position error, scalability, and communication and computational requirements. Early simulations yield average position errors of 5 in the presence of both range and initial position inaccuracies. Physicists recently observed that realistic complex networks emerge as discrete samples from a continuous hyperbolic geometry enclosed in a circle: the radius represents the node centrality and the angular displacement between two nodes resembles their topological proximity. The hyperbolic circle aims to become a universal space of representation and analysis of many real networks. Yet, inferring the angular coordinates to map a real network back to its latent geometry remains a challenging inverse problem. Here, we show that intelligent machines for unsupervised recognition and visualization of similarities in big data can also infer the network angular coordinates of the hyperbolic model according to a geometrical organization that we term “angular coalescence.” Based on this phenomenon, we propose a class of algorithms that offers fast and accurate “coalescent embedding” in the hyperbolic circle even for large networks. This computational solution to an inverse problem in physics of complex systems favors the application of network latent geometry techniques in disciplines dealing with big network data analysis including biology, medicine, and social science. Mapping complex networks to underlying geometric spaces can help understand the structure of networked systems. Here the authors propose a class of machine learning algorithms for efficient embedding of large real networks to the hyperbolic space, with potential impact on big network data analysis.