Network flow algorithms and applications

This paper looks at several methods for solving network flow problems. The first chapter gives a brief background for linear programming (LP) problems. It includes basic definitions and theorems. The second chapter gives an overview of graph theory including definitions, theorems, and examples.

Chapters 3-5 are the heart of this thesis. Chapter 3 includes algorithms and applications for maximum flow problems. It includes a look at a very important theorem. Maximum Flow/Minimum Cut Theorem. There is also a section on the Augmenting Path Algorithm. Chapter 4 Deals with shortest path problem. It includes Dijsksta's Algorithm and the All-Pairs Labeling Algorithm. Chapter 5 includes information on algorithms and applications for the minimum cost flow(MCF)problem. The algorithms covered include the Cycle Canceling,Successive ShortestPath,and Primal-Dual Algorithms. Each of these chapters 3-5 contain definitions,theorems,and algorithms to solve network flow problems.

Throughout the paper the computer program LINDO is used. It serves a couple of functions. First it is a way of checking each solution. The second use is to expose the reader to a very valuable tool in linear programming.