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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| Vydané v: | Operations research letters Ročník 49; číslo 2; s. 270 - 277 |
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| Hlavní autori: | , , |
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Elsevier B.V
01.03.2021
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| 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. |
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| AbstractList | 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. |
| Author | Tsidulko, Oxana Yu van Bevern, René Afanasev, Vsevolod A. |
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| Cites_doi | 10.1002/net.21985 10.1016/j.jcss.2016.06.001 10.1002/net.3230170304 10.1287/opre.43.3.399 10.1287/opre.9.6.841 10.1006/jcss.2001.1774 10.1002/net.3230060305 10.1016/j.hm.2020.04.003 10.1007/BF01580113 10.1016/0305-0483(73)90089-3 10.1016/0167-6377(91)90016-I 10.1016/j.tcs.2016.04.006 10.1090/S0002-9939-1956-0078686-7 10.1016/j.ejor.2004.06.003 10.1016/S0377-2217(02)00813-5 10.1007/BF01442866 10.1016/S0167-6377(99)00046-2 10.1137/0208031 |
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| Keywords | NP-hardness Temporal graphs Arc routing Approximation algorithm Rural Postman Problem Fixed-parameter algorithm |
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| SubjectTerms | Approximation algorithm Arc routing Fixed-parameter algorithm NP-hardness Rural Postman Problem Temporal graphs |
| Title | The Hierarchical Chinese Postman Problem: The slightest disorder makes it hard, yet disconnectedness is manageable |
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