An algorithm for exact rectilinear Steiner trees for switchbox with obstacles

The switchbox rectilinear Steiner tree problem is to construct an optimal rectilinear Steiner tree interconnecting n terminals on the perimeter of a switchbox without crossing any obstacles inside the switchbox. However, intersecting boundaries of obstacles are allowed. 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, m Steiner trees are generated in O(mn) time, and the best one among them is selected