Creating and exploiting flexibility in rectilinear Steiner trees

Creating and Exploiting Flexibility in Steiner Trees

The Steiner tree problem for terminals on the boundary of a rectilinear polygon

Given a simple rectilinear polygon P with k sides and n terminals on its boundary, we present an O(k 3 n)-time algorithm to compute the minimal rectilinear Steiner tree lying inside P interconnecting the terminals. We obtain our result by proving structural properties of a selective set of minimal Steiner trees and exploiting them in a dynamic programming algorithm.

A catalog of Hanan grid problems

We present a general rectilinear Steiner tree problem in the plane and prove that it is solvable on the Hanan grid of the input points. This result is then used to show that several variants of the ordinary rectilinear Steiner tree problem are solvable on the Hanan grid, including | but not limited to | Steiner trees for rectilinear (or iso-thetic) polygons, obstacle-avoiding Steiner trees, gro...

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 ...

The Steiner Ratio for Obstacle-Avoiding Rectilinear Steiner Trees

We consider the problem of finding a shortest rectilinear Steiner tree for a given set of points in the plane in the presence of rectilinear obstacles that must be avoided. We extend the Steiner ratio to the obstacle-avoiding case and show that it is equal to the Steiner ratio for the obstacle-free case.