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."
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