The Hierarchical Chinese Postman Problem: The slightest disorder makes it hard, yet disconnectedness is manageable - Afanasev, Vsevolod A.; van Bevern, René; Tsidulko, Oxana Yu (Operations research letters, 2021)
The Hierarchical Chinese Postman Problem is finding a shortest traversal of all edges of a graph respecting precedence constraints given by a partial order on classes of edges. We show that the special case with connected classes is NP-hard even on orders decomposable into a chain and an incomparable class. For the case with linearly ordered (possibly disconnected) classes, we get 5/3-approximations and fixed-parameter algorithms by transferring results from the Rural Postman Problem.