Spanning Trees and Optimization Problems

Preface The research on spanning trees has been one of the most important areas in algorithm design. People who are interested in algorithms will find this book informative and inspiring. The new results are still accumulating, and we try to make clear the whole picture of the current status and future developments. This book is written for graduate or advanced undergraduate students in computer science, electrical engineering, industrial engineering, and mathematics. It is also a good reference for professionals. Our motivations for writing this book: 1. To the best of our knowledge, there is no book totally dedicated to the topics of spanning trees. 2. Our recent progress in spanning trees reveals a new line of investigation. 3. Designing approximation algorithms for spanning tree problems has become an exciting and important field in theoretical computer science. 4. Besides numerous network design applications, spanning trees have also been playing important roles in newly established research areas, such as biological sequence alignments, and evolutionary tree construction. This book is a general and rigorous text on algorithms for spanning trees. It covers the full spectrum of spanning tree algorithms from classical computer science to modern applications. The selected topics in this book make it an excellent handbook on algorithms for spanning trees. At the end of every chapter, we report related work and recent progress. We first explain general properties of spanning trees. We then focus on three categories of spanning trees, namely, minimum spanning trees, shortest-paths trees, and optimum routing cost spanning trees. We also show how to balance the tree costs. Besides the theoretical description of the methods, many examples are used to illustrate the ideas behind them. Moreover, we demonstrate some applications of these spanning trees. We explore in details some other interesting spanning trees, including maximum leaf spanning trees and minimum diameter spanning trees. In addition, Steiner trees and evolutionary trees are also discussed. We close this book by summarizing other important problems related to spanning trees. Writing a book is not as easy as we thought at the very beginning of this project. We have tried our best to make it consistent and correct. However, it's a mission impossible for imperfect authors to produce a perfect book. vii viii Preface Should you find any mathematical, historical, or typographical errors, please let us know. We are extremely grateful to Richard Chia-Tung Lee, Webb Miller, and Chuan Yi Tang, who …