From Few Components to an Eulerian Graph by Adding Arcs
Eulerian Extension (EE) is the problem to make an arc-weighted directed multigraph Eulerian by adding arcs of minimum total cost. EE is NP-hard and has been shown fixed-parameter tractable with respect to the number of arc additions. Complementing this result, on the way to answering an open question, we show that EE is fixed-parameter tractable with respect to the combined parameter “number of connected components in the underlying undirected multigraph” and “sum of indeg(v) - outdeg(v) over all vertices v in the input multigraph where this value is positive.” Moreover, we show that EE is unlikely to admit a polynomial-size problem kernel for this parameter combination and for the parameter “number of arc additions”.
KeywordsWeight Function Initial Vertex Terminal Vertex Input Instance Positive Balance
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- 8.Frederickson, G.N.: Approximation Algorithms for NP-hard Routing Problems. PhD thesis, Faculty of the Graduate School of the University of Maryland (1977)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
- 13.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, Available electronically. arXiv:1101.4283 [cs.DM] (2011)Google Scholar
- 17.Sorge, M., van Bevern, R., Niedermeier, R., Weller, M.: A New View on Rural Postman Based on Eulerian Extension and Matching. In: Iliopoulos, C.S. (ed.) IWOCA 2011. LNCS, vol. 7056, pp. 310–323. Springer, Heidelberg (2011)Google Scholar