I'm going to assume that (a) you want to minimize the number of sensors used and (b) there is no limit to the number of devices to which one sensor can be connected. (The second assumption seems shaky to me, but you did not mention a limit.) Under those assumptions, your problem can be reduced to an uncapacitated facility location problem (UFLP), in which each sensor type is a "facility", each device is a "customer", customers (devices) can only be assigned to compatible facilities (sensor types), and the objective is to minimize the number of facilities (sensor types). Given a solution, you just install one sensor of each selected type and hook it to the devices specified by the solution. This can be easily modified to minimize the cost of the selected sensors, if different types have different costs.
I'm pretty sure the UFLP is NP-hard, and since your problem is equivalent to it, that should mean no polynomial time exact solution is possible.
If you have a limit on how many devices one sensor can support, you can tweak the model to make it a capacitated FLP by allowing a predefined number of sensors of each type (for instance five type A sensors, assuming that five would be enough to handle every type A-compatible device). You might want to throw in some antisymmetry constraints to improve model solution time.
Polynomial time heuristics can of course be cobbled together, with no guarantee of optimality.