Finding a Maximum Value Flow in Pure Network : DINIC'S METHOD FOR FINDING A MAXIMUM VALUE FLOW IN PURE NETWORK

Optimizing (maximizing or minimizing) is a basic need of human being. There are many real life problems that need the process of optimization; one of it is the problem of finding a maximum value flow in a single commodity network. A maximum value flow in a pure network can be calculated by different methods with different computational complexity. One of the earliest methods is the Ford-Fulkerson Algorithm with limited practical use. Hence, among the different methods this book emphasized on Dinic's method for getting a maximum value flow in pure network (single commodity flow) with very best running time. The method is applied after constructing an auxiliary network (layered network) with respect to the present flow vector in a given network. This process identifies and includes those paths which are important for maximizing the flow amount in the network. To get the maximum value flow, the construction step of the layered network would be carried out repeatedly. The book clearly shows how to use the Dinic's method appropriately and contains clear examples for elaborating the means to get a maximum value flow by the aforementioned method.