We are given a set of sensors at given locations, a set of potential
locations for placing base stations (BSs, or sinks), and another set of
potential locations for placing wireless relay nodes. There is a cost for
placing a BS and a cost for placing a relay. The problem we consider is to
select a set of BS locations, a set of relay locations, and an association of
sensor nodes with the selected BS locations, so that number of hops in the path
from each sensor to its BS is bounded by hmax, and among all such feasible
networks, the cost of the selected network is the minimum. The hop count bound
suffices to ensure a certain probability of the data being delivered to the BS
within a given maximum delay under a light traffic model. We observe that the
problem 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 earlier
work, along with a modification of the greedy algorithm for weighted set cover.
We have analyzed the worst case approximation guarantee for this algorithm. We
have also proposed a polynomial time heuristic to improve upon the solution
provided by SmartSelect. Our numerical results demonstrate that the algorithms
provide good quality solutions using very little computation time in various
randomly generated network scenarios
