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This paper study two problems that arise in optimization of sensor networks: First, we devise provable approximation schemes for locating a base station and constructing a network among a set of sensors each of which has a data stream to get to the base station. Subject to power constraints at the sensors, our goal is to locate the base station and establish a network in order to maximize the lifespan of the network. Second, we study optimal sensor placement problems for quality coverage of given domains cluttered with obstacles. We assume "line-of-site", sensors, that sense a point only if the straight segment connecting the sensor to this point (the "line-of-site") does not cross any obstacle. so obstacles occludes area from using line-of-site sensors, the goal is to minimize the number of sensors required in order to have each point "well covered" according to precise criteria (e.g., that each point is seen by two sensors that form at least angle a, or that each point is seen by three sensors that form a triangle containing the point).