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We are given a set of sensors at given locations, a set of potentiallocations for placing base stations (BSs, or sinks), and another set ofpotential locations for placing wireless relay nodes. There is a cost forplacing a BS and a cost for placing a relay. The problem we consider is toselect a set of BS locations, a set of relay locations, and an association ofsensor nodes with the selected BS locations, so that number of hops in the pathfrom each sensor to its BS is bounded by hmax, and among all such feasiblenetworks, the cost of the selected network is the minimum. The hop count boundsuffices to ensure a certain probability of the data being delivered to the BSwithin a given maximum delay under a light traffic model. We observe that theproblem is NP-Hard, and is hard to even approximate within a constant factor.For this problem, we propose a polynomial time approximation algorithm(SmartSelect) based on a relay placement algorithm proposed in our earlierwork, along with a modification of the greedy algorithm for weighted set cover.We have analyzed the worst case approximation guarantee for this algorithm. Wehave also proposed a polynomial time heuristic to improve upon the solutionprovided by SmartSelect. Our numerical results demonstrate that the algorithmsprovide good quality solutions using very little computation time in variousrandomly generated network scenarios.

QoS Constrained Optimal Sink and Relay Placement in Planned Wireless Sensor Networks