Computing Optimal Rectilinear Steiner Trees: A Survey and Experimental Evaluation

The rectilinear Steiner tree problem is to nd a minimum-length rectilinear interconnection of a set of points in the plane. A reduction from the rectilinear Steiner tree problem to the graph Steiner tree problem allows the use of exact algorithms for the graph Steiner tree problem to solve the rectilinear problem. Furthermore, a number of more direct, geometric algorithms have been devised for computing optimal rectilinear Steiner trees. This paper surveys algorithms for computing optimal rectilinear Steiner trees and presents experimental results comparing nine of them: graph Steiner tree algorithms due to Beasley, Bern, Dreyfus and Wagner, Hakimi, and Shore, Foulds, and Gibbons and geometric algorithms due to Ganley and Cohoon, Salowe and Warme, and Thomborson, Alpern, and Carter.