A modified Hopfield network for two-dimensional module placement

The problem of two-dimensional module placement is solved using a Hopfield network with the objective of minimizing total wire-length. The network is modified to include quartic terms in its energy functional by making the interconnection matrix dependent on the state of the network. This modification decomposes the two-dimensional problem into two coupled one-dimensional problems. A hierarchical approach based on min-cut placement is used to make the network size grow linearly with the number of modules. Computer simulations of the network show that it is capable of finding good solutions that are competitive with well-known heuristic algorithms, particularly when a probabilistic update rule is used for the neurons to avoid local minima. The network can be easily modified to accommodate hard placement of nodules, unequal module sizes, and the constraints of I/O (input/output) pad connections