Abstract
Eulerian extension problems aim at making a given (directed) (multi-)graph Eulerian by adding a minimum-cost set of edges (arcs). These problems have natural applications in scheduling and routing and are closely related to the Chinese Postman and Rural Postman problems. Our main result is to show that the NP-hard Weighted Multigraph Eulerian Extension is fixed-parameter tractable with respect to the number k of extension edges (arcs). For an n-vertex multigraph, the corresponding running time amounts to O(4k ·n 3). This implies a fixed-parameter tractability result for the “equivalent” Rural Postman problem. In addition, we present several polynomial-time algorithms for natural Eulerian extension problems.
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Dorn, F., Moser, H., Niedermeier, R., Weller, M. (2010). Efficient Algorithms for Eulerian Extension. In: Thilikos, D.M. (eds) Graph Theoretic Concepts in Computer Science. WG 2010. Lecture Notes in Computer Science, vol 6410. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-16926-7_11
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DOI: https://doi.org/10.1007/978-3-642-16926-7_11
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