Path Partition in Directed Graph ? Modeling and Optimization

The concept of graph theory is therefore perfectly suitable to structure a problem in its initial analysis phases since a graph is the most general mathematical object. At the structural level, the nodes represent the objects, the variables… and the arc forms the binary relation of influence among them. Many real problems can be modeled as path partition in directed graph that played particular role in the operation of arranging a set of nodes especially in case of directed acyclic graph (DAG). We encounter such graph in schedule problems, the analysis of language structure, the probability theory, the game theory, compilers…. Moreover managerial problem can be modeled as acyclic graphs, also the potential problem has a suitable solution if and only if the graph is acyclic.