On Optimal Arrangements of Binary Sensors

A large range of monitoring applications can benefit from binary sensor networks. Binary sensors can detect the presence or absence of a particular target in their sensing regions. They can be used to partition a monitored area and provide localization functionality. If many of these sensors are deployed to monitor an area, the area is partitioned into sub-regions: each sub-regions is characterized by the sensors detecting targets within it. We aim to maximize the number of unique, distinguishable sub-regions. Our goal is an optimal placement of both omni-directional and directional static binary sensors. We compute an upper bound on the number of unique sub-regions, which grows quadratically with respect to the number of sensors. In particular, we propose arrangements of sensors within a monitored area whose number of unique sub-regions is asymptotically equivalent to the upper bound.