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Network of unmanned vehicles, are poised to be the next giant leap of technology. Such systems are already being used by the defense and law enforcement agencies. The US DoD and some very large private corporations are spending large sums of money for developing intellectual properties that will assist in implementing such systems. Amazon is testing its own drones for delivery whereas Google, Tesla, Ford and Mercedes Benz are investing in self driving cars, that can operate in real traffic conditions. Their goal is to make the vehicles either operate in a standalone mode or in collaboration with other similar vehicles. This push towards the use of unmanned systems comes with its own set of new problems. Most of these problems would require solutions in real time. This has created a lot of scope for innovative research using these networks and the research problems fall broadly into two categories: the first relates to the development of hardware and robotics, which is concerned with building better hardware to implement such systems. The second category is concerned with the design and implementation of efficient algorithms, that work with the implemented hardware. These algorithms in turn belong to three broad categories, namely: navigation and localization algorithms, algorithms for dynamic topology determination for efficient communication and information exchange, consensus algorithms for multi-sensor data fusion that in turn help in navigation and localization. In this thesis we consider four problems of interest, each of which belongs to one of these categories: first we consider the problem of GPS-denied navigation using signals of opportunity, which belongs to the class of algorithms for navigation and localization. Next we consider two problems from the second category. More precisely we consider the problem of spanners, which are sparse subgraphs of an input graph having nice structural properties. We study two variations of the spanner problem: the first one arises in communication networks and aims to guarantee the communication efficiency of a sparse subgraph of the input and the second one studies construction of spanners having robustness guarantees. Finally, we consider algorithms for truth determination from multiple sources, which is a type of consensus algorithm.
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