Efficient Algorithms for Eulerian Extension

  • Frederic Dorn
  • Hannes Moser
  • Rolf Niedermeier
  • Mathias Weller
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6410)


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(4 k ·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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© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • Frederic Dorn
    • 1
  • Hannes Moser
    • 2
  • Rolf Niedermeier
    • 2
  • Mathias Weller
    • 2
  1. 1.Department of InformaticsUniversity of BergenNorway
  2. 2.Institut für InformatikFriedrich-Schiller-Universität JenaJenaGermany

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