Rectilinear Full Steiner Tree Generation Rectilinear Full Steiner Tree Generation

The fastest exact algorithm (in practice) for the rectilinear Steiner tree problem in the plane uses a two-phase scheme: First a small but suucient set of full Steiner trees (FSTs) is generated and then a Steiner minimum tree is constructed from this set by using simple backtrack search, dynamic programming or an integer programming formulation. FST generation methods can be seen as problem reduction algorithms and are also useful as a rst step in providing good upper-and lower-bounds for large instances. Currently, the time needed to generate FSTs poses a signii-cant overhead for FST based exact algorithms. In this paper we present a very eecient algorithm for the rectilinear FST generation problem which removes this overhead completely. Based on information obtained in a preprocessing phase, the new algorithm \grows" FSTs while applying several new and important optimality conditions. For randomly generated instances approximately 4n FSTs are generated (where n is the number of terminals). The observed running time is quadratic and the FSTs for a 10000 terminal instance can on average be generated within 10 minutes.