On Optimal Sensor Placement with Hypercube Cutting Planes

We study the problem of locating sensors to detect the failure of any set of radiation sources in a system. For computing illumination data, we suggest the use of radiosity methods. We then consider the problem of optimising sensor placement to unambiguously identify any inactive sources. 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. Also, we outline an approach to estimate the size of the input space.