In this chapter, some applications of network flow problems are addressed based on each type of problem being discussed. For example, in the case of shortest path problems, their concept in facility layout, facility location, robotics, transportation, and very large-scale integration areas are pointed out in the first section. Furthermore, the second section deals with the implementation of the maximum flow problem in image segmentation, transportation, web communities, and wireless networks and telecommunication areas. Moreover, in the third section, the minimum-cost flow problem is discussed in fleeting and routing problems, petroleum, and scheduling areas. Meanwhile, a brief explanation about each application as well as some corresponding literature and research papers are presented in each section. In addition, based on available literature in each of these areas, some research gaps are identified, and future trends as well as chapter’s conclusion are pointed out in the fourth section.
This chapter gives the basic introduction to directed graphs (digraphs) and their pertinent concepts, elements, and frameworks. From a general point of view, the most majority of concepts of digraphs have similar characteristics with networks structures. Therefore, in conjunction with networks chapter, this chapter not only emphasizes some aspect of digraphs, but also addresses the basic terminology and terms that have been widely applied in literature. Regarding this premise, the first section presents the basic definitions, and the second section classifies the most important and applicable types of digraphs extensively addressed in the literature. Moreover, one of the main concepts of digraphs (reachability and connectivity) is discussed in the third section. In addition, the fourth section briefly discusses a few application cases of digraphs, and the fifth section finally presents the conclusion of this chapter.
This chapter sheds light on various aspects of network theory and relevant concepts including basic definitions, the most common types of network flow problems that have been studied by literature, and the main algorithms and solution approaches proposed for solving network problems.
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