Discrete sensor placement problems in distribution networks

We consider the problem of placing sensors in a network to detect and identify the source of any contamination. We consider two variants of this problem: 1) sensorconstrained : we are allowed a fixed number of sensors and want to minimize contamination detection time; and 2) time-constrained : we must detect contamination within a given time limit and want to minimimize the number of sensors required. Our main results are as follows. First, we give a necessary and sufficient condition Preprint submitted to Elsevier Science 15 December 2004 for source identification. Second, we show that the sensor and time constrained versions of the problem are polynomially equivalent. Finally, we show that the sensorconstrained version of the problem is polynomially equivalent to the asymmetric k-center problem and that the time-constrained version of the problem is polynomially equivalent to the dominating set problem.