The upper bound neural network and a class of consistent labeling problems

The upper bound neural network (UBNN) is proposed for solving a class of consistent labeling problems (CLP). Crossbar switching is used as an illustration. The set of stable attractors of the dynamical system is identically the set of feasible solutions to the problem. CLP is a general class of NP-complete (Neyman-Pearson) problems intersecting artificial intelligence, symbolic logic, and operations research. Problems which can be formulated as CLP include image segmentation as well as finding spanning trees and Euler tours in a graph. As an example, the UBNN is used to control a crossbar packet switch. The switch control problem is a maximal matching problem which is approximated by the UBNN. As switching speeds push below the nanosecond range, the O(V³) time complexity of the maximal matching problem will be prohibitive for large switches. When viewed as an analog circuit, the UBNN scales well, guarantees convergence to a solution of the problem, and converges in near constant time, thus becoming an alternative for large crossbar switch control