A parallel Steiner tree heuristic for macro cell routing

Global routing of macro cells remains an important but time-consuming step in the VLSI design cycle. Macro cells are large, irregularly sized parameterized circuit modules that typically contain large numbers of terminals that must be interconnected. The interconnection pattern for each set of terminals (net) that must be connected is a Steiner tree, and the primary sub-problem in the global routing of macro cells is to find a set of dissimilar, low-cost Steiner trees for each net that must be routed. In this paper, a two-phase, parallel (multi-processor) algorithm is proposed for quickly constructing a diverse pool of high-quality Steiner trees for routing of multi-terminal nets. In the first phase, a single Steiner tree is constructed using a heuristic, called Shrubbery. Then, in the second phase, a pool of dissimilar, high-quality trees are created from the original tree, by running multiple instances of a local search in parallel. Computational experiments performed on over 800 commonly used benchmarks show that running multiple instances of the local search in parallel results in near-linear speed-up over the serial case. Most importantly, the trees produced are both high-quality and dissimilar, allowing for numerous routing possibilities for each net.