An Algorithm for Exact Rectilinear Steiner Trees for Switchbox with Obstacles

Abstract

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 is allowed. We present an algorithm that computes an optimal switchbox rectilinear Steiner tree in O(F<inf>1</inf>(k)n + F<inf>2</inf>(k)) time, where k is the number of obstacles inside the switchbox and F<inf>1</inf> and F<inf>2</inf> are exponential functions of k. For any constant k, the proposed algorithm runs in O(n) time. As an immediate extension, we can generate m Steiner trees in O(mn) time, and among them, select the best one. © 1992 IEEE