In recent years, algorithmic graph theory has become increasingly important as a link between discrete mathematics and theoretical computer science. This textbook introduces students of mathematics and computer science to the interrelated fields of graphs theory, algorithms and complexity.

The Steiner problem asks for a shortest network which spans a given set of points. Minimum spanning networks have been well-studied when all connections are required to be between the given points. The novelty of the Steiner tree problem is that new auxiliary points can be introduced between the original points so that a spanning network of all the points will be shorter than otherwise possible. These new points are called Steiner points - locating them has proved problematic and research has diverged along many different avenues. This volume is devoted to the assimilation of the rich field of intriguing analyses and the consolidation of the fragments. A section has been given to each of the three major areas of interest which have emerged. The first concerns the Euclidean Steiner Problem, historically the original Steiner tree problem proposed by Jarník and Kössler in 1934. The second deals with the Steiner Problem in Networks, which was propounded independently by Hakimi and Levin and has enjoyed the most prolific research amongst the three areas. The Rectilinear Steiner Problem, introduced by Hanan in 1965, is discussed in the third part. Additionally, a forth section has been included, with chapters discussing areas where the body of results is still emerging. The collaboration of three authors with different styles and outlooks affords individual insights within a cohesive whole.

The Steiner tree problem is one of the most important combinatorial optimization problems. It has a long history that can be traced back to the famous mathematician Fermat (1601-1665). This book studies three significant breakthroughs on the Steiner tree problem that were achieved in the 1990s, and some important applications of Steiner tree problems in computer communication networks researched in the past fifteen years. It not only covers some of the most recent developments in Steiner tree problems, but also discusses various combinatorial optimization methods, thus providing a balance between theory and practice.

This book constitutes the refereed proceedings of the 8th Scandinavian Workshop on Algorithm Theory, SWAT 2002, held in Turku, Finland, in July 2002. The 43 revised full papers presented together with two invited contributions were carefully reviewed and selected from 103 submissions. The papers are organized in topical sections on scheduling, computational geometry, graph algorithms, robotics, approximation algorithms, data communication, computational biology, and data storage and manipulation.

The design of approximation algorithms for spanning tree problems has become an exciting and important area of theoretical computer science and also plays a significant role in emerging fields such as biological sequence alignments and evolutionary tree construction. While work in this field remains quite active, the time has come to collect under

The Volume on Advances in Steiner Trees is divided into two sections. The first section of the book includes papers on the general geometric Steiner tree problem in the plane and higher dimensions. The second section of the book includes papers on the Steiner problem on graphs. The general geometric Steiner tree problem assumes that you have a given set of points in some d-dimensional space and you wish to connect the given points with the shortest network possible. The given set ofpoints are 3 Figure 1: Euclidean Steiner Problem in E usually referred to as terminals and the set ofpoints that may be added to reduce the overall length of the network are referred to as Steiner points. What makes the problem difficult is that we do not know a priori the location and cardinality ofthe number ofSteiner points. Thus)the problem on the Euclidean metric is not known to be in NP and has not been shown to be NP-Complete. It is thus a very difficult NP-Hard problem.

One of Springer’s renowned Major Reference Works, this awesome achievement provides a comprehensive set of solutions to important algorithmic problems for students and researchers interested in quickly locating useful information. This first edition of the reference focuses on high-impact solutions from the most recent decade, while later editions will widen the scope of the work. All entries have been written by experts, while links to Internet sites that outline their research work are provided. The entries have all been peer-reviewed. This defining reference is published both in print and on line.