Differential privacy in networked data collection

The problem of destination privacy in networked data collection is investigated under constraints on routing overhead. Using differential privacy as a metric to quantify the privacy of the intended destination, optimal probabilistic routing schemes are investigated under unicast and multicast paradigms. When the overhead is weighted equally to the incurred routing cost to intended destination, it is shown that the optimal solution for unicast private routing is identical to a traveling sales man solution. When the overhead weight is strictly different to the intended routing cost, the optimal solution is expressed as a solution to a linear programming problem. It is shown that the optimal solution can be implemented in decentralized manner. Under a multicast paradigm, the optimal solution when overhead is weighted equal to the intended cost, the optimal solution is shown to be a variant of the Steiner tree problem. In general, it is proved that multicast private routing is an np-complete problem. Simulations and numerical results for both private unicast and multicast routing on random graphs are presented.