## Rectilinear Full Steiner Tree Generation (1997)

Venue: | NETWORKS |

Citations: | 27 - 5 self |

### BibTeX

@ARTICLE{Zachariasen97rectilinearfull,

author = {Martin Zachariasen},

title = {Rectilinear Full Steiner Tree Generation},

journal = {NETWORKS},

year = {1997},

volume = {33},

pages = {125--143}

}

### OpenURL

### Abstract

The fastest exact algorithm (in practice) for the rectilinear Steiner tree problem in the plane uses a two-phase scheme: First a small but sufficient 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 first step in providing good upper- and lower-bounds for large instances. Currently, the time needed to generate FSTs poses a significant overhead for FST based exact algorithms. In this paper we present a very efficient 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 o...