Linear gate assignment: a fast statistical mechanics approach

This paper deals with the problem of linear gate assignment in two layout styles: one-dimensional logic array and gate matrix layout. The goal is to find the optimal sequencing of gates in order to minimize the required number of tracks, and thus to reduce the overall circuit layout area. This is known to be an NP-hard optimization problem, for which no absolute approximation algorithm exists. Here we report the use of a new optimization heuristic derived from statistical mechanics-the microcanonical optimization algorithm, μ0-to solve the linear gate assignment problem. Our numerical results show that μ0 compares favorably with at least five previously employed heuristics: simulated annealing, the unidirectional and the bidirectional Hong construction methods, and the artificial intelligence heuristics GM Plan and GM Learn. We also show how the algorithm is able to outperform microcanonical annealing. Moreover, in a massive set of experiments with circuits whose optimal layout is not known, our algorithm has been able to match and even to improve, by as much as seven tracks, the best solutions known so far