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Geometric Graph Theory And Wireless Sensor Networks, Deniz Sarioz

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In this work, we apply geometric and combinatorial methods to explore a variety of problems motivated by wireless sensor networks. Imagine sensors capable of communicating along straight lines except through obstacles like buildings or barriers, such that the communication network topology of the sensors is their visibility graph. Using a standard distributed algorithm, the sensors can build common knowledge of their network topology.

We first study the following inverse visibility problem: What positions of sensors and obstacles define the computed visibility graph, with fewest obstacles? This is the problem of finding a minimum obstacle representation of a graph. This minimum …