Network Optimization

The mathematical science behind network analysis and network optimization is the graph theory. In computing, topology is useful to understand networks, the flow of information throughout the network, or paths within a system. The Seven Bridges of Konigsberg is similar to another common problem in network optimization called Traveling Salesman Problem (TSP), where one try to find the most efficient route given a set of places to visit, with some restrictions, just like in the seven bridges problem. This chapter covers some of the algorithms such as the TSP, Shortest Path, Minimum Cost Network Flow, Minimum Cut, Minimum Spanning Tree, and Vehicle Routing Problem (VRP). Maximum network flow can be used in airline scheduling or image segmentation. Maximum flow problems involve finding a feasible flow throughout a flow network that obtains the maximum possible flow rate. The VRP can be used to find the best dispatch for goods from depots to customers.