Networks and Graphs

Dr Smith here presents essential mathematical and computational ideas of network optimisation for senior undergraduate and postgraduate students in mathematics, computer science and operational research. He shows how algorithms can be used for finding optimal paths and flows, identifying trees in networks, and optimal matching. Later chapters discuss postman and salesperson tours, and demonstrate how many network problems are related to the ‘‘minimal-cost feasible-flow’’ problem. Techniques are presented both informally and with mathematical rigour and aspects of computation, especially of complexity, have been included. Numerous examples and diagrams illustrate the techniques and applications. The book also includes problem exercises with tutorial hints.

• Presents essential mathematical and computational ideas of network optimisation for senior undergraduate and postgraduate students in mathematics, computer science and operational research
• Demonstrates how algorithms can be used for finding optimal paths and flows, identifying trees in networks and optimal matching
• Numerous examples and diagrams illustrate the techniques and applications

Senior undergraduate students and graduate students in mathematics, computer science, and operational research

Ideas and definitions; Trees; Shortest paths; Maximum flows; How to store a network; More about shortest paths; Advanced maximal flow; Minimal-cost, feasible-flow; Matching and assignment; Postman problems; Travelling salesperson problems; Tutorial hints; References; Index.