Chinese Postman Problem

This article describes one of the classical routing problems—Chinese postman problem (CPP). The objective of CPP is to determine a closed walk of minimum length covering each arc on the graph at least once. Five types of CPP based on the properties of graphs are discussed: Undirected CPP, directed CPP, mixed CPP, windy postman problem (WPP), and hierarchical postman problem (HPP). The first two types of problems are polynomially solvable while the other three are proved to be NP-hard. Available mathematical models and algorithms are summarized for each problem type. This article also presents some variations of the CPP and recent results from the literature.