title: Inhibitory grids and the assignment problem.
abstract: A family of symmetric neural networks that solve a simple version of the assignment problem (AP) is analyzed. The authors analyze the suboptimal performance of these networks and compare the results to optimal answers obtained by linear programming techniques. They then use the interactive activation model to define the network dynamics-a model that is closely related to the Hopfield-Tank model. A systematic analysis of hypercube corner stability and eigenspaces of the connection strength matrix leads to network parameters that give feasible solutions 100% of the time and to a projection algorithm that significantly improves performance. Two formulations of the problem are discussed: (i) nearest corner: encode the assignment numbers as initial activations, and (ii) lowest energy corner: encode the assignment numbers as external inputs.
authors.affiliation: Dept. of Comput. Sci. and Eng., Colorado Univ., Denver, CO.
authors.forename: W J
authors.initials: WJ
authors.lastname: Wolfe
authors.forename: J M
authors.initials: JM
authors.lastname: Macmillan
authors.forename: G
authors.initials: G
authors.lastname: Brady
authors.forename: R
authors.initials: R
authors.lastname: Mathews
authors.forename: J A
authors.initials: JA
authors.lastname: Rothman
authors.forename: D
authors.initials: D
authors.lastname: Mathis
authors.forename: M D
authors.initials: MD
authors.lastname: Orosz
authors.forename: C
authors.initials: C
authors.lastname: Anderson
authors.forename: G
authors.initials: G
authors.lastname: Alaghband