The Hierarchical Chinese Postman Problem: the slightest disorder makes it hard, yet disconnectedness is manageable
arXiv:2011.04022 · doi:10.1016/j.orl.2021.01.017
Abstract
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.
Fixed Figure 4 and an argument in the proof of Lemma 3.7(iii)