Abstract

This dissertation examines the geometric Steiner tree problem: given a set of terminals in the plane, find a minimum-length interconnection of those terminals according to some geometric distance metric. In the process, however, it addresses a much more general and widely applicable problem, that of finding a minimum-weight spanning tree in a hypergraph. The geometric Steiner tree problem is known to be NP-complete for the rectilinear metric, and NP-hard for the Euclidean metric. The fastest exact algorithms (in practice) for these problems use two phases: First a small but sufficient set of full Steiner trees (FSTs) is generated and then a Steiner minimal tree is constructed from this set. These phases are called FST generation and FST concatenation, respectively, and an overview of each phase is presented. FST concatenation is almost always the most expensive phase, and has traditionally been accomplished via simple backtrack search or dynamic programming.

Citations