Spanning Trees and Optimization Problems
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Spanning Trees and Optimization Problems

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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 problemsshow more

Product details

  • Hardback | 200 pages
  • 163.6 x 242.3 x 16.5mm | 421.85g
  • Taylor & Francis Inc
  • Chapman & Hall/CRC
  • Boca Raton, FL, United States
  • English
  • New.
  • 67 black & white illustrations, 1 black & white tables
  • 1584884363
  • 9781584884361

Review quote

"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. 3show more

Table of contents

SPANNING TREES Counting Spanning Trees MINIMUM SPANNING TREES Introduction Bor uvka's Algorithm Prim's Algorithm Kruskal's Algorithm Applications Summary Bibliographic Notes and Further Reading Exercises SHORTEST-PATHS TREES Introduction Dijkstra's Algorithm The Bellman-Ford Algorithm Applications Summary Bibliographic Notes and Further Reading 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 Bibliographic Notes and Further Reading Exercises OPTIMAL COMMUNICATION SPANNING TREES Introduction Product-Requirement Sum-Requirement Multiple Sources Applications Summary Bibliographic Notes and Further Reading Exercises BALANCING THE TREE COSTS Introduction Light Approximate Shortest-Paths Trees Light Approximate Routing Cost Spanning Trees Applications Summary Bibliographic Notes and Further Reading Exercises STEINER TREES AND SOME OTHER PROBLEMS Steiner Minimal Trees Trees and Diameters Maximum Leaf Spanning Trees Some Other Problems Bibliographic Notes and Further Reading Exercises REFERENCES INDEXshow more