An exact algorithm for the construction of rectilinear steiner minimum trees among complex obstacles

In this paper, we present an exact algorithm for the construction of obstacle-avoiding rectilinear Steiner minimum trees (OARSMTs) among complex rectilinear obstacles. This is the first work to propose a geometric approach to optimally solve the OARSMT problem among complex obstacles. The optimal solution is constructed by the concatenation of full Steiner trees (FSTs) among complex obstacles, which are proven to be of simple structures in this paper. The algorithm is able to handle complex obstacles including both convex and concave ones. Benchmarks with hundreds of terminals among a large number of obstacles are solved optimally in a reasonable amount of time.