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:Operations research letters Vol. 49; no. 2; pp. 270 - 277
Main Authors: Afanasev, Vsevolod A., van Bevern, René, Tsidulko, Oxana Yu
Format: Journal Article
Language:English
Published: Elsevier B.V 01.03.2021
Subjects:
Approximation algorithm
Arc routing
Fixed-parameter algorithm
NP-hardness
Rural Postman Problem
Temporal graphs
NP-hardness
Temporal graphs
Arc routing
Approximation algorithm
Rural Postman Problem
Fixed-parameter algorithm
ISSN:0167-6377, 1872-7468
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:0167-6377
1872-7468
DOI:10.1016/j.orl.2021.01.017