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 incomparabl...

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Bibliographic Details
Published in:arXiv.org 2021-01
Main Authors: Afanasev, Vsevolod A, René van Bevern, Oxana Yu Tsidulko
Format: Article
Language:English
Subjects:
Algorithms
Graph theory
Precedence constraints
Online Access:Get full text
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Summary: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.
ISSN:2331-8422
DOI:10.48550/arxiv.2011.04022