Christie Recent advances in statistical physics based on the concept of the renormalization group are applied to the problem of computer interconnection optimization. This enables a thermodynamic model of system connectivity to be developed which is consistent with the hierarchical boundary conditions imposed by the rack-board-chip method of computer construction. From this theoretical description a new optimization algorithm, called geometrical annealing, is proposed. In contrast to other thermodynamically based algorithms, geometrical annealing acknowledges the spatial relationships that exist between optimal wire length arrangements by employing minimization routines based on geometrical principles. It is anticipated that this property may hold the key to matching the performance of experienced human designers who naturally employ their spatial awareness in producing efficient wiring layouts. Other benefits of this research will include a deeper understanding of the relationship between statistical mechanics and combinatorial optimization, the thermodynamic justification of the power-law relationship between connectivity and system size, known as Rent's rule, and the development of new thermodynamic relationships between the parameters which characterize hierarchically structured systems.
