A Practical Introduction to Data Structures and Algorithm Analysis

11GraphsGraphs provide the ultimate in data structure flexibility. Graphs can model bothreal-world systems and abstract problems, so they are used in hundreds of applications.Here is a small sampling of the range of problems that graphs are appliedto.1. Modeling connectivity in computer and communications networks.2. Representing a map as a set of locations with distances between locations;used to compute shortest routes between locations.3. Modeling flow capacities in transportation networks.4. Finding a path from a starting condition to a goal condition; for example, inartificial intelligence problem solving.5. Modeling computer algorithms, showing transitions from one program stateto another.6. Finding an acceptable order for finishing subtasks in a complex activity, suchas constructing large buildings.7. Modeling relationships such as family trees, business or military organizations,and scientific taxonomies.We begin in Section 11.1 with some basic graph terminology and then definetwo fundamental representations for graphs, the adjacency matrix and adjacencylist. Section 11.2 presents a graph ADT and simple implementations based on theadjacency matrix and adjacency list. Section 11.3 presents the two most commonlyused graph traversal algorithms, called depth-first and breadth-first search, withapplication to topological sorting. Section 11.4 presents algorithms for solvingsome problems related to finding shortest routes in a graph. Finally, Section 11.5presents algorithms for finding the minimum-cost spanning tree, useful for determininglowest-cost connectivity in a network. Besides being useful and interestingin their own right, these algorithms illustrate the use of some data structures presentedin earlier chapters.389