 |  Introduction to Algorithms, 2/e Thomas H. Cormen,
Dartmouth College
Charles E. Leiserson,
Massachusetts Institute of Technology
Ronald L. Rivest,
Massachusetts Institute of Technology
Clifford Stein,
Columbia University
Elementary Graph Algorithms
Chapter Overview - Chapter 22| This chapter presents methods for representing a graph and for searching a graph. Searching a graph means systematically following the edges of the graph so as to visit the vertices of the graph. A graph-searching algorithm can discover much about the structure of a graph. Many algorithms begin by searching their input graph to obtain this structural information. Other graph algorithms are organized as simple elaborations of basic graph-searching algorithms. Techniques for searching a graph are at the heart of the field of graph algorithms.
Section 22.1 discusses the two most common computational representations of graphs: as adjacency lists and as adjacency matrices. Section 22.2 presents a simple graph-searching algorithm called breadth-first search and shows how to create a breadth-first tree. Section 22.3 presents depth-first search and proves some standard results about the order in which depth-first search visits vertices. Section 22.4 provides our first real application of depth-first search: topologically sorting a directed acyclic graph. A second application of depth-first search, finding the strongly connected components of a directed graph, is given in Section 22.5. |
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2002 McGraw-Hill Higher Education