Towards optimal sensor placement with hypercube cutting planes

We study the problem of locating sensors to detect the state of any set of radiation sources in a system. To compute illumination data, we propose the use of radiosity methods. Considering the problem of optimizing sensor placement to identify any inactive sources unambiguously, we show that the problem can be transformed from a numerical to a geometrical domain, relate it to set covering, and then attempt to transform it into the domain of graphs. We present some results on hypercube cutting planes that help us progress towards the latter transformation by characterizing its combinatorial structure. We also outline how to estimate the size of the input space.