Spanning Trees and Optimization Problems

TL;DR: This chapter discusses Spanning Trees, a system for maximizing the efficiency of the Spanning Tree Algorithm by minimizing the number of components.

Abstract: SPANNING TREES Counting Spanning Trees MINIMUM SPANNING TREES Introduction Bor Degreesuvka'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 INDEX