Abstract
The majority of arc routing problems can be viewed as variants of the classical Chinese Postman Problem (CPP). Restating the generic problem, let G = (V,E) be a connected graph (undirected) with V a finite set (the nodes) and E ⊂ V × V be the set of edges. In addition, we have a real valued weight (distance) W ij ≥ 0, ∀(i, j) ∈E, and a design problem: “Construct a least distance traversal sequence of all the edges in E starting at and returning to the same node.” This is in essence the Chinese Postman Problem as posed by Meigu Guan (Mei-Ko Kwan) in 1962, in the Chinese Mathematics journal which is the main reason why we refer to this problem as the CPP. The historical overview of arc routing and variants of CPP are eloquently described by Eiselt and Laporte (this book), however we examine the Guan (1962) work for its illustration of the computational aspects when solving the CPP and related problems. As pointed out in Edmonds and Johnson (1973), the CPP can be separated into two parts: given an arbitrary (connected) graph G, duplicate a set of edges in E of minimal total weight to transform G into Ĝ (an even degree graph) which admits an Euler tour (a closed tour which traverses exactly once every edge in the graph), and then construct an Euler tour on Ĝ.
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