Best Response Dynamics for VLSI Physical Design Placement

Abstract

The physical design placement problem is one of the hardest and most important problems in micro chips production. The placement defines how to place the electrical components on the chip. We consider the problem as a combinatorial optimization problem, whose instance is defined by a set of 2-dimensional rectangles, with various sizes and wire connectivity requirements. We focus on minimizing the placement area and the total wire-length.We propose a local-search method for coping with the problem, based on natural dynamics common in game theory. Specifically, we suggest to perform variants of Best-Response Dynamics (BRD). In our method, we assume that every component is controlled by a selfish agent, who aim at minimizing his individual cost, which depends on his own location and the wire-length of his connections.We suggest several BRD methods, based on selfish migrations of a single or a cooperative of components. We performed a comprehensive experimental study on various test-benches, and compared our results with commonly known algorithms, in particular, with simulated annealing. The results show that selfish local-search, especially when applied with cooperatives of components, may be beneficial for the placement problem.