The Steiner ratio
This is a monograph describing recent research developments on the Steiner ratio, the least upper bound for ratio of lengths between the Steiner minimum tree and the minimum spanning tree for the same set of points in a certain metric space. Determing the Steiner ratio in each metric space is a classic combinatorial research problem in many metric spaces, the problem is quite hard. Indeed, the Steiner ratio is not determined for a large number of spaces. There are many unsolved conjectures concerning the value of the Steiner ratio and its bounds. This book consists of 12 chapters collecting almost all existing results on the Steiner ratio except (1) the Steiner ratio on surfaces and (2) the lower bound 0.615 for the Steiner ratio in any Euclidean space. Overall, this is a very valuable reference book for researchers interested in Steiner trees and the Steiner ratio.
scientific article; zbMATH DE number 1734451