Ebook: The Steiner Tree Problem: A Tour through Graphs, Algorithms, and Complexity

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. No specific previous knowledge is assumed.
The central theme of the book is a geometrical problem dating back to Jakob Steiner. This problem, now called the Steiner problem, was initially of importance only within the context of land surveying. In the last decade, however, applications as diverse as VLSI-layout and the study of phylogenetic trees led to a rapid rise of interest in this problem. The resulting progress has uncovered fascinating connections between and within graph theory, the study of algorithms, and complexity theory. This single problem thus serves to bind and motivate these areas. The book's topics include: exact algorithms, computational complexity, approximation algorithms, the use of randomness, limits of approximability.
A special feature of the book is that each chapter ends with an "excursion" into some related area. These excursions reinforce the concepts and methods introduced for the Steiner problem by placing them in a broader context.

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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. No specific previous knowledge is assumed.
The central theme of the book is a geometrical problem dating back to Jakob Steiner. This problem, now called the Steiner problem, was initially of importance only within the context of land surveying. In the last decade, however, applications as diverse as VLSI-layout and the study of phylogenetic trees led to a rapid rise of interest in this problem. The resulting progress has uncovered fascinating connections between and within graph theory, the study of algorithms, and complexity theory. This single problem thus serves to bind and motivate these areas. The book's topics include: exact algorithms, computational complexity, approximation algorithms, the use of randomness, limits of approximability.
A special feature of the book is that each chapter ends with an "excursion" into some related area. These excursions reinforce the concepts and methods introduced for the Steiner problem by placing them in a broader context.

---

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. No specific previous knowledge is assumed.
The central theme of the book is a geometrical problem dating back to Jakob Steiner. This problem, now called the Steiner problem, was initially of importance only within the context of land surveying. In the last decade, however, applications as diverse as VLSI-layout and the study of phylogenetic trees led to a rapid rise of interest in this problem. The resulting progress has uncovered fascinating connections between and within graph theory, the study of algorithms, and complexity theory. This single problem thus serves to bind and motivate these areas. The book's topics include: exact algorithms, computational complexity, approximation algorithms, the use of randomness, limits of approximability.
A special feature of the book is that each chapter ends with an "excursion" into some related area. These excursions reinforce the concepts and methods introduced for the Steiner problem by placing them in a broader context.



Content:
Front Matter....Pages I-VIII
Basics I: Graphs....Pages 1-22
Basics II: Algorithms....Pages 23-40
Basics III: Complexity....Pages 41-62
Special Terminal Sets....Pages 63-74
Exact Algorithms....Pages 75-86
Approximation Algorithms....Pages 87-106
More on Approximation Algorithms....Pages 107-132
Randomness Helps....Pages 133-164
Limits of Approximability....Pages 165-190
Geometric Steiner Problems....Pages 191-222
Back Matter....Pages 223-243

---

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. No specific previous knowledge is assumed.
The central theme of the book is a geometrical problem dating back to Jakob Steiner. This problem, now called the Steiner problem, was initially of importance only within the context of land surveying. In the last decade, however, applications as diverse as VLSI-layout and the study of phylogenetic trees led to a rapid rise of interest in this problem. The resulting progress has uncovered fascinating connections between and within graph theory, the study of algorithms, and complexity theory. This single problem thus serves to bind and motivate these areas. The book's topics include: exact algorithms, computational complexity, approximation algorithms, the use of randomness, limits of approximability.
A special feature of the book is that each chapter ends with an "excursion" into some related area. These excursions reinforce the concepts and methods introduced for the Steiner problem by placing them in a broader context.



Content:
Front Matter....Pages I-VIII
Basics I: Graphs....Pages 1-22
Basics II: Algorithms....Pages 23-40
Basics III: Complexity....Pages 41-62
Special Terminal Sets....Pages 63-74
Exact Algorithms....Pages 75-86
Approximation Algorithms....Pages 87-106
More on Approximation Algorithms....Pages 107-132
Randomness Helps....Pages 133-164
Limits of Approximability....Pages 165-190
Geometric Steiner Problems....Pages 191-222
Back Matter....Pages 223-243
....