A new view on rural postman based on Eulerian extension and matching

Manuel Sorge; René Van Bevern; Rolf Niedermeier; Mathias Weller

doi:10.1007/978-3-642-25011-8_25

A new view on rural postman based on Eulerian extension and matching

Manuel Sorge, René Van Bevern, Rolf Niedermeier, Mathias Weller

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

3 Scopus citations

Abstract

We provide a new characterization of the NP-hard arc routing problem Rural Postman in terms of a constrained variant of minimum-weight perfect matching on bipartite graphs. To this end, we employ a parameterized equivalence between Rural Postman and Eulerian Extension, a natural arc addition problem in directed multigraphs. We indicate the NP-hardness of the introduced matching problem. In particular, we use it to make some partial progress towards answering the open question about the parameterized complexity of Rural Postman with respect to the number of weakly connected components in the graph induced by the required arcs. This is a more than thirty years open and long-time neglected question with significant practical relevance.

Original language	English
Title of host publication	Combinatorial Algorithms - 22nd International Workshop, IWOCA 2011, Revised Selected Papers
Pages	310-323
Number of pages	14
DOIs	https://doi.org/10.1007/978-3-642-25011-8_25
State	Published - 28 Nov 2011
Externally published	Yes
Event	22nd International Workshop on Combinatorial Algorithms, IWOCA 2011 - Vancouver, BC, Canada Duration: 20 Jul 2011 → 22 Jul 2011

Publication series

Name	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume	7056 LNCS
ISSN (Print)	0302-9743
ISSN (Electronic)	1611-3349

Conference

Conference	22nd International Workshop on Combinatorial Algorithms, IWOCA 2011
Country/Territory	Canada
City	Vancouver, BC
Period	20/07/11 → 22/07/11

ASJC Scopus subject areas

Theoretical Computer Science
Computer Science (all)

Access to Document

10.1007/978-3-642-25011-8_25

Cite this

Sorge, M., Van Bevern, R., Niedermeier, R., & Weller, M. (2011). A new view on rural postman based on Eulerian extension and matching. In Combinatorial Algorithms - 22nd International Workshop, IWOCA 2011, Revised Selected Papers (pp. 310-323). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 7056 LNCS). https://doi.org/10.1007/978-3-642-25011-8_25

Sorge, Manuel ; Van Bevern, René ; Niedermeier, Rolf et al. / A new view on rural postman based on Eulerian extension and matching. Combinatorial Algorithms - 22nd International Workshop, IWOCA 2011, Revised Selected Papers. 2011. pp. 310-323 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).

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abstract = "We provide a new characterization of the NP-hard arc routing problem Rural Postman in terms of a constrained variant of minimum-weight perfect matching on bipartite graphs. To this end, we employ a parameterized equivalence between Rural Postman and Eulerian Extension, a natural arc addition problem in directed multigraphs. We indicate the NP-hardness of the introduced matching problem. In particular, we use it to make some partial progress towards answering the open question about the parameterized complexity of Rural Postman with respect to the number of weakly connected components in the graph induced by the required arcs. This is a more than thirty years open and long-time neglected question with significant practical relevance.",

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Sorge, M, Van Bevern, R, Niedermeier, R & Weller, M 2011, A new view on rural postman based on Eulerian extension and matching. in Combinatorial Algorithms - 22nd International Workshop, IWOCA 2011, Revised Selected Papers. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 7056 LNCS, pp. 310-323, 22nd International Workshop on Combinatorial Algorithms, IWOCA 2011, Vancouver, BC, Canada, 20/07/11. https://doi.org/10.1007/978-3-642-25011-8_25

A new view on rural postman based on Eulerian extension and matching. / Sorge, Manuel; Van Bevern, René; Niedermeier, Rolf et al.
Combinatorial Algorithms - 22nd International Workshop, IWOCA 2011, Revised Selected Papers. 2011. p. 310-323 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 7056 LNCS).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

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AB - We provide a new characterization of the NP-hard arc routing problem Rural Postman in terms of a constrained variant of minimum-weight perfect matching on bipartite graphs. To this end, we employ a parameterized equivalence between Rural Postman and Eulerian Extension, a natural arc addition problem in directed multigraphs. We indicate the NP-hardness of the introduced matching problem. In particular, we use it to make some partial progress towards answering the open question about the parameterized complexity of Rural Postman with respect to the number of weakly connected components in the graph induced by the required arcs. This is a more than thirty years open and long-time neglected question with significant practical relevance.

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Sorge M, Van Bevern R, Niedermeier R, Weller M. A new view on rural postman based on Eulerian extension and matching. In Combinatorial Algorithms - 22nd International Workshop, IWOCA 2011, Revised Selected Papers. 2011. p. 310-323. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). doi: 10.1007/978-3-642-25011-8_25

A new view on rural postman based on Eulerian extension and matching

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