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We study the problem of wireless sensor network design by deploying a minimumnumber of additional relay nodes (to minimize network cost) at a subset ofgiven potential relay locations, in order to convey the data from alreadyexisting sensor nodes (hereafter called source nodes) to a Base Station, whilemeeting a certain specified hop count bound (the hop count bound is chosen toensure a pre-determined probability of the data being delivered to the BSwithin a given maximum delay). We study two variations of the problem.  First we sudy the problem of guaranteed QoS connected network design, wherethe objective is to have at least one path from each source to the BS with thespecified hop count bound. We show that the problem is NP-Hard. For a problemin which the number of existing sensor nodes and potential relay locations isn, we propose an O(n) approximation algorithm of polynomial time complexity.Results show that the algorithm performs efficiently (in over 90% of the testedscenarios, it gave solutions that were either optimal or were worse thanoptimal by just one relay) in various randomly generated network scenarios.  Next, we study the problem of survivable network design with guaranteed QoS,i.e, the requirement is to have at least k > 1 node disjoint hop constrainedpaths from each source to the BS. We show that the problem is NP-Hard. We alsoshow that the problem of finding a feasible solution to this optimizationproblem is NP-Complete. We propose two polynomial time heuristics for thisproblem, and compare their performance on various randomly generated networkscenarios.

QoS Aware and Survivable Network Design for Planned Wireless Sensor Networks