Synthesis of simple distributed detection networks

The article studies algorithmic issues of simple object detection problems in the context of a system consisting of a finite set of sensors S that monitor a workspace. Each sensor a∈S detects the presence of any object that belongs to a certain subset, Det(a), of a given set of objects O. The detection problem is defined as follows: given that an object had been detected at a subset D⊆S of sensors, identify if the object in the workspace could be a member of O. If yes, compute the maximal set of such members. If not, declare the object in the workspace to be unidentified. Two versions are considered of this problem based on how the input is specified. In the forward detection problem, one is given {Det(a)}_a∈S . In the backward detection problem, one is given {Set(b)}_b∈O, where Set(b) is the set of sensors at which the object b∈O would be detected. The article constructs a conceptual graph structure called the detection network that yields efficient implementation of detection algorithms using combinational circuits, message-based systems and parallel computing systems. It shows the problem of computing a network with minimum number of edges is computationally intractable, and then presents several polynomial-time approximation algorithms. Then it presents sequential algorithms to solve the detection problems with and without preprocessing. It also discusses parallel algorithms on shared memory systems and hypercube-based message passing systems. Finally, it shows that the problem of recognizing multiple objects is computationally intractable