A new class of iterative Steiner tree heuristics with good performance

A fast approach to the minimum rectilinear Steiner tree (MRST) problem is presented. The method yields results that reduce wire length by up to 2% to 3% over the previous methods, and is the first heuristic which has been shown to have a performance ratio less than 3/2; in fact, the performance ratio is less than or equal to 4/3 on the entire class of instances where the ratio c(MST)/c(MRST) is exactly equal to 3/2. The algorithm has practical asymptotic complexity owing to an elegant implementation which uses methods from computation geometry and which parallelizes readily. A randomized variation of the algorithm, along with a batched variant, has also proved successful