Parameterized Directed $k$-Chinese Postman Problem and $k$ Arc-Disjoint Cycles Problem on Euler Digraphs
Abstract
In the Directed -Chinese Postman Problem (-DCPP), we are given a connected weighted digraph and asked to find non-empty closed directed walks covering all arcs of such that the total weight of the walks is minimum. Gutin, Muciaccia and Yeo (Theor. Comput. Sci. 513 (2013) 124--128) asked for the parameterized complexity of -DCPP when is the parameter. We prove that the -DCPP is fixed-parameter tractable. We also consider a related problem of finding arc-disjoint directed cycles in an Euler digraph, parameterized by . 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.
Cite
@article{arxiv.1402.2137,
title = {Parameterized Directed $k$-Chinese Postman Problem and $k$ Arc-Disjoint Cycles Problem on Euler Digraphs},
author = {Gregory Gutin and Mark Jones and Bin Sheng and Magnus Wahlstrom},
journal= {arXiv preprint arXiv:1402.2137},
year = {2014}
}