Multi-level Steiner Trees

Two-level rectilinear Steiner trees

Given a set P of terminals in the plane and a partition of P into k subsets P1, . . . , Pk, a two-level rectilinear Steiner tree consists of a rectilinear Steiner tree Ti connecting the terminals in each set Pi (i = 1, . . . , k) and a top-level tree Ttop connecting the trees T1, . . . , Tk. The goal is to minimize the total length of all trees. This problem arises naturally in the design of lo...

Steiner Trees and Steiner Forests

Pseudo-Gilbert-Steiner trees

The Gilbert network problem is a generalization of the Steiner minimal tree problem derived by adding flow-dependent weights to the edges. In this paper, we define a special class of minimum Gilbert networks, called pseudo-Gilbert–Steiner trees, and we show that it can be constructed by Gilbert’s generalization of Melzak’s method. Besides, a counterexample, a pseudo-Gilbert–Steiner tree, is con...

Preferred Direction Steiner Trees

The planar rectilinear Steiner tree problem has been extensively studied. The common formulation ignores circuit fabrication issues such as multiple routing layers, preferred routing directions, and vias between layers. In this paper, the authors extend a previously presented planar rectilinear Steiner tree heuristic to consider layer assignment, preferred routing direction restrictions, and vi...

Steiner trees and polyhedra