Optimal Interconnection Trees in the Plane

Marcus Brazil is Associate Professor and Reader at the Melbourne School of Engineering, The University of Melbourne, with a background in pure mathematics. He has worked on Steiner trees and network optimization problems for about 18 years, and has written more than 60 papers in this area, both on the theory of optimal network design and on industrial applications to Wireless Sensor Networks, Telecommunications, VLSI Physical Design, and Underground Mining Planning. Martin Zachariasen is Head of Department and Professor at the Department of Computer Science, University of Copenhagen. He has worked on heuristics and exact methods for classical NP-hard problems, such as the geometric Steiner Tree Problem, as well as other optimization problems. His general research interests are in experimental algorithmics and computational combinatorial optimization, in particular related to VLSI design. As well as writing more than 40 papers on these topics, he is one of the developers of GeoSteiner, which is by far the most efficient software for solving a range of geometric Steiner tree problems.

Preface:- 1 Euclidean and Minkowski Steiner Trees.- 2 Fixed Orientation Steiner Trees.- 3 Rectilinear Steiner Trees.- 4 Steiner Trees with Other Costs and Constraints.- 5 Steiner Trees in Graphs and Hypergraphs.- A Appendix.

"The book presents an interesting and quickly developing area of research and will be useful for researchers working in this area and for those wanting to learn more about geometric Steiner tree problems." (Yongtang Shi, Mathematical Reviews, December, 2015)

"The focus of this monograph is the geometric Steiner tree problem, i.e., how to optimally connect, in a geometric plane, a collection of n given terminals, together with an additional set of Steiner points, in terms of a measuring metric. ... monograph is also intended as a textbook at a graduate level, thus comes with a decent collection of exercises, with varying difficulty degrees, at the end of each chapter, mostly assigned in a relevant context throughout the main text." (Zhizhang Shen, zbMATH 1319.05044, 2015)