Chinese Postman Problem

Abstract

One of the very popular applications of the graph theory in real world problems is related to the concept of Eulerian tours and trails introduced in Eulerian trail and tours chapter. There are many problems in which users should serve all the connections (edges in a graph, streets of a city, pipelines of a network and etc.) between nodes. In chapter 7 of this book, the existence of such trails and tours in graphs were discussed, and appropriate algorithms were introduced to find Eulerian trails and tour. But in the case a graph does not have such a tour or trail, it’s important to traverse some edges more than once, and this is what usually happens in real world applications. M.K. Kwan in 1962 was the first who introduced this problem as the Chinese postman problem (CPP). The question was that, given a postal zone with a number of streets that must be served by a postal carrier, how can one develop a tour that covers every street in the zone and brings the postman back to his or her point of origin, having traveled the minimum possible distance (Wang et al., 2008)? In this chapter, the Chinese postman problem is discussed, and different variations of it are introduced. Then the very early form of the CPP in which the graph is undirected is explained in more detail.