Approximation Algorithms for Some Postman Problems
Journal of the ACM (JACM)
Parameterized Complexity Theory (Texts in Theoretical Computer Science. An EATCS Series)
Parameterized Complexity Theory (Texts in Theoretical Computer Science. An EATCS Series)
New heuristic algorithms for the windy rural postman problem
Computers and Operations Research - Articles presented at the conference on routing and location (CORAL)
Efficient algorithms for Eulerian extension
WG'10 Proceedings of the 36th international conference on Graph-theoretic concepts in computer science
From few components to an eulerian graph by adding arcs
WG'11 Proceedings of the 37th international conference on Graph-Theoretic Concepts in Computer Science
A new view on Rural Postman based on Eulerian Extension and Matching
Journal of Discrete Algorithms
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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.