Efficient algorithms for Eulerian extension

Authors:
Frederic Dorn;Hannes Moser;Rolf Niedermeier;Mathias Weller
Affiliations:
Department of Informatics, University of Bergen, Norway;Institut für Informatik, Friedrich-Schiller-Universität Jena, Jena, Germany;Institut für Informatik, Friedrich-Schiller-Universität Jena, Jena, Germany;Institut für Informatik, Friedrich-Schiller-Universität Jena, Jena, Germany
Venue:
WG'10 Proceedings of the 36th international conference on Graph-theoretic concepts in computer science
Year:
2010

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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 ċ n3). 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.