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- W1815974477 abstract "In the Directed $$k$$ -Chinese Postman Problem ( $$k$$ -DCPP), we are given a connected weighted digraph $$G$$ and asked to find $$k$$ non-empty closed directed walks covering all arcs of $$G$$ such that the total weight of the walks is minimum. Gutin, Muciaccia and Yeo (Theor. Comput. Sci. 513, 124–128 (2013)) asked for the parameterized complexity of $$k$$ -DCPP when $$k$$ is the parameter. We prove that the $$k$$ -DCPP is fixed-parameter tractable. We also consider a related problem of finding $$k$$ arc-disjoint directed cycles in an Euler digraph, parameterized by $$k$$ . Slivkins (ESA 2003) showed that this problem is W[1]-hard for general digraphs. Generalizing another result by Slivkins, we prove that the problem is fixed-parameter tractable for Euler digraphs. The corresponding problem on vertex-disjoint cycles in Euler digraphs remains W[1]-hard even for Euler digraphs." @default.
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- W1815974477 date "2014-01-01" @default.
- W1815974477 modified "2023-09-27" @default.
- W1815974477 title "Parameterized Directed $$k$$-Chinese Postman Problem and $$k$$ Arc-Disjoint Cycles Problem on Euler Digraphs" @default.
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- W1815974477 doi "https://doi.org/10.1007/978-3-319-12340-0_21" @default.
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