The Hierarchical Chinese Postman Problem: The Slightest Disorder Makes It Hard, Yet Disconnectedness Is Manageable

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. (C) 2021 Elsevier B.V. All rights reserved.