# The Hierarchical Chinese Postman Problem: the slightest disorder makes it hard, yet disconnectedness is manageable

arXiv: https://arxiv.org/abs/2011.04022 · HTML: https://mlsanity.com/paper/2011.04022/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 8 Nov 2020.

## Built on by (most cited first, 1 of 1)

- [Hybridising Reinforcement Learning and Heuristics for Hierarchical Directed Arc Routing Problems](https://mlsanity.com/paper/2501.00852/) (2025)

## Abstract (arXiv)

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.