A New View on Rural Postman Based on Eulerian Extension and Matching
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.
KeywordsManifold Cabral Plowing
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- 1.Assad, A.A., Golden, B.L.: Arc routing methods and applications. In: Network Routing. Handbooks in Operations Research and Management Science, vol. 8, pp. 375–483. Elsevier B.V. (1995)Google Scholar
- 6.Dror, M.: Arc Routing: Theory, Solutions, and Applications. Kluwer Academic Publishers (2000)Google Scholar
- 10.Höhn, W., Jacobs, T., Megow, N.: On Eulerian extensions and their application to no-wait flowshop scheduling. J. Sched (to appear, 2011)Google Scholar
- 12.Niedermeier, R.: Invitation to Fixed-Parameter Algorithms. Oxford University Press (2006)Google Scholar
- 16.Sorge, M.: On making directed graphs Eulerian. Diplomarbeit, Institut für Informatik, Friedrich-Schiller-Universität Jena (2011), Available electronically. arXiv:1101.4283 [cs.DM]Google Scholar