1st Edition

# Spanning Trees and Optimization Problems

By Bang Ye Wu, Kun-Mao Chao Copyright 2004
200 Pages 67 B/W Illustrations
by Chapman & Hall

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 one cover spanning tree properties, classical results, and recent research developments.

Spanning Trees and Optimization Problems offers the first complete treatment of spanning tree algorithms, from their role in classical computer science to their most modern applications. The authors first explain the general properties of spanning trees, then focus on three main categories: minimum spanning trees, shortest-paths trees, and minimum routing cost spanning trees. Along with the theoretical descriptions of the methods, numerous examples and applications illustrate the concepts in practice. The final chapter explores several other interesting spanning trees, including maximum leaf spanning trees, minimum diameter spanning trees, Steiner trees, and evolutionary trees.

With logical organization, well chosen topics, and easy to understand pseudocode, the authors provide not only a full, rigorous treatment of theory and applications, but also an excellent handbook for spanning tree algorithms. This book will be a welcome addition to your reference shelf whether your interests lie in graph and approximation algorithms for theoretical work or you use graph techniques to solve practical problems

SPANNING TREES
Counting Spanning Trees
MINIMUM SPANNING TREES
Introduction
Bor°uvka's Algorithm
Prim's Algorithm
Kruskal's Algorithm
Applications
Summary
Exercises
SHORTEST-PATHS TREES
Introduction
Dijkstra's Algorithm
The Bellman-Ford Algorithm
Applications
Summary
Exercises
MINIMUM ROUTING COST SPANNING TREES
Introduction
Approximating by a Shortest-Paths Tree
Approximating by a General Star
A Reduction to the Metric Case
A Polynomial Time Approximation Scheme
Applications
Summary
Exercises
OPTIMAL COMMUNICATION SPANNING TREES
Introduction
Product-Requirement
Sum-Requirement
Multiple Sources
Applications
Summary
Exercises
BALANCING THE TREE COSTS
Introduction
Light Approximate Shortest-Paths Trees
Light Approximate Routing Cost Spanning Trees
Applications
Summary
Exercises
STEINER TREES AND SOME OTHER PROBLEMS
Steiner Minimal Trees
Trees and Diameters
Maximum Leaf Spanning Trees
Some Other Problems
Exercises
REFERENCES
INDEX

### Biography

Wu\, Bang Ye; Chao\, Kun-Mao

"… will supplement nicely undergraduate courses in discrete mathematics and graph theory … Summing Up: … Recommended for upper-division undergraduates through faculty."
- CHOICE, November 2004, Vol. 42, No. 3