An algorithm for exact rectilinear Steiner trees for switchbox with obstacles

The switchbox rectilinear Steiner tree problem, which is to construct an optimal rectilinear Steiner tree interconnecting n terminals on the perimeter of a switchbox without crossing any obstacles inside the switchbox, is addressed. An algorithm that computes an optimal switchbox rectilinear Steiner tree in O(F₁(k)n+F₂ (k)) time, where k is the number of obstacles inside the switchbox and F₁ and F₂ are exponential functions of k, is presented. For any constant k, the proposed algorithm runs in O(n) time. As an immediate extension, it is possible to generate m Steiner trees in O(mn) time and select the best one among them