The random deployment of Wireless Sensor and Actuator Network (WSAN) nodes in areas often inaccessible, results in so-called coverage holes – i.e. areas in the network that are not adequately covered by nodes to suit the requirements of the network. Various coverage protocol algorithms have been designed to reduce or eliminate coverage holes within WSANs by indicating how to move the nodes. The effectiveness of such coverage protocols could be jeopardised by inaccuracy in the initial node location data that is broadcast by the respective nodes. This study examines the effects of location inaccuracies on five sensor deployment and reconfiguration algorithms – They include two algorithms which assume that mobile nodes are deployed (referred to as the VEC and VOR algorithms); two that assume static nodes are deployed (referred to as the CNPSS and OGDC algorithms); and a single algorithm (based on a bidding protocol) that assumes a hybrid scenario in which both static and mobile nodes are deployed. Two variations of this latter algorithm are studied. A location simulation tool was built using the GE Smallworld GIS application and the Magik programming language. The simulation results are based on three above-mentioned deployment scenarios; mobile, hybrid and static. The simulation results suggest the VOR algorithm is reasonably robust if the location inaccuracies are somewhat lower than the sensing distance and also if a high degree of inaccuracy is limited to a relatively small percentage of the nodes. The VEC algorithm is considerably less robust, but prevents nodes from drifting beyond the boundaries in the case of large inaccuracies. The bidding protocol used by the hybrid algorithm appears to be robust only when the static nodes are accurate and there is a low degree of inaccuracy within the mobile nodes. Finally the static algorithms are shown to be the most robust; the CPNSS algorithm appears to be immune to location inaccuracies whilst the OGDC algorithm was shown to reduce the number of active nodes in the network to a better extent than that of the CPNSS algorithm. Copyright / Dissertation (MSc)--University of Pretoria, 2010. / Computer Science / unrestricted

Les algorithmes distribués de consensus sont des algorithmes itératifs de faible complexité où les nœuds de capteurs voisins interagissent les uns avec les autres pour parvenir à un accord commun sans unité coordinatrice. Comme les nœuds dans un réseau de capteurs sans fil ont une puissance de calcul et une batterie limitées, ces algorithmes distribués doivent parvenir à un consensus en peu de temps et avec peu d’échange de messages. La première partie de cette thèse s’est basée sur l’étude et la comparaison des différents algorithmes de consensus en mode synchrone et asynchrone en termes de vitesse de convergence et taux de communications. La seconde partie de nos travaux concerne l’application de ces algorithmes de consensus au problème de la détection de trous de couverture dans les réseaux de capteurs sans fil.Ce problème de couverture fournit aussi le contexte de la suite de nos travaux. Il se décrit comme étant la façon dont une région d’intérêt est surveillée par des capteurs. Différentes approches géométriques ont été proposées mais elles sont limitées par la nécessité de connaitre exactement la position des capteurs ; or cette information peut ne pas être disponible si les dispositifs de localisation comme par exemple le GPS ne sont pas sur les capteurs. À partir de l’outil mathématique appelé topologie algébrique, nous avons développé un algorithme distribué de détection de trous de couverture qui recherche une fonction harmonique d’un réseau, c’est-à-dire annulant l’opérateur du Laplacien de dimension 1. Cette fonction harmonique est reliée au groupe d’homologie H1 qui recense les trous de couverture. Une fois une fonction harmonique obtenue, la détection des trous se réalise par une simple marche aléatoire dans le réseau. / Distributed consensus algorithms are iterative algorithms of low complexity where neighboring sensors interact with each other to reach an agreement without coordinating unit. As the nodes in a wireless sensor network have limited computing power and limited battery, these distributed algorithms must reach a consensus in a short time and with little message exchange. The first part of this thesis is based on the study and comparison of different consensus algorithms synchronously and asynchronously in terms of convergence speed and communication rates. The second part of our work concerns the application of these consensus algorithms to the problem of detecting coverage holes in wireless sensor networks.This coverage problem also provides the context for the continuation of our work. This problem is described as how a region of interest is monitored by sensors. Different geometrical approaches have been proposed but are limited by the need to know exactly the position of the sensors; but this information may not be available if the locating devices such as GPS are not on the sensors. From the mathematical tool called algebraic topology, we have developed a distributed algorithm of coverage hole detection searching a harmonic function of a network, that is to say canceling the operator of the 1-dimensional Laplacian. This harmonic function is connected to the homology group H1 which identifies the coverage holes. Once a harmonic function obtained, detection of the holes is realized by a simple random walk in the network.