This book is a collection of articles studying various Steiner tree prob lems with
applications in industries such as the design of electronic cir cuits computer networking
telecommunication and perfect phylogeny. The Steiner tree problem was initiated in the
Euclidean plane. Given a set of points in the Euclidean plane the shortest network
interconnect ing the points in the set is called the Steiner minimum tree. The Steiner minimum
tree may contain some vertices which are not the given points. Those vertices are called
Steiner points while the given points are called terminals. The shortest network for three
terminals was first studied by Fermat (1601-1665). Fermat proposed the problem of finding a
point to minimize the total distance from it to three terminals in the Euclidean plane. The
direct generalization is to find a point to minimize the total distance from it to n terminals
which is still called the Fermat problem today. The Steiner minimum tree problem is an indirect
generalization. Schreiber in 1986 found that this generalization (i.e. the Steiner mini mum
tree) was first proposed by Gauss.
