On the performance bounds for a class of rectilinear Steiner tree heuristics in arbitrary dimension

A family of examples on which a large class C of minimum spanning tree-based rectilinear Steiner tree heuristics has a performance ratio arbitrarily close to 3/2 times optimal is given. The class C contains many published heuristics whose worst-case performance ratios were previously unknown. Of particular interest is that C contains two heuristics whose worst-case ratios had been conjectured to be bounded away from 3/2, and the construction also points out an incorrect claim of optimality for one of these heuristics. The examples also force the worst possible behavior in a number of heuristics outside C. The construction generalizes to d dimensions, where the heuristics will have performance ratios of at least 2d - 1/d; this improves the previous lower bound on performance ratio in arbitrary dimension