Parameterized complexity of the MINCCA problem on graphs of bounded decomposability

In an edge-colored graph, the cost incurred at a vertex on a path when two incident edges with different colors are traversed is called reload or changeover cost. The Minimum Changeover Cost Arborescence (MinCCA) problem consists in finding an arborescence with a given root vertex such that the tota...

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Bibliographic Details
Published in:Theoretical computer science Vol. 690; pp. 91 - 103
Main Authors: Gözüpek, Didem, Özkan, Sibel, Paul, Christophe, Sau, Ignasi, Shalom, Mordechai
Format: Journal Article
Language:English
Published: Elsevier B.V 22.08.2017
Elsevier
Subjects:
[formula omitted] algorithm
Mathematics
Minimum changeover cost arborescence
Parameterized complexity
Planar graph
Tree-cutwidth
Treewidth
Tree-cutwidth
Minimum changeover cost arborescence
FPT algorithm
Planar graph
Parameterized complexity
Treewidth
ISSN:0304-3975, 1879-2294
Online Access:Get full text
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Summary:In an edge-colored graph, the cost incurred at a vertex on a path when two incident edges with different colors are traversed is called reload or changeover cost. The Minimum Changeover Cost Arborescence (MinCCA) problem consists in finding an arborescence with a given root vertex such that the total changeover cost of the internal vertices is minimized. It has been recently proved by Gözüpek et al. (2016) that the MinCCA problem when parameterized by the treewidth and the maximum degree of the input graph is in FPT. In this article we present the following hardness results for MinCCA:•the problem is W[1]-hard when parameterized by the vertex cover number of the input graph, even on graphs of degeneracy at most 3. In particular, it is W[1]-hard parameterized by the treewidth of the input graph, which answers the main open problem in the work of Gözüpek et al. (2016);•it is W[1]-hard on multigraphs parameterized by the tree-cutwidth of the input multigraph; and•it remains NP-hard on planar graphs even when restricted to instances with at most 6 colors and 0/1 symmetric costs, or when restricted to instances with at most 8 colors, maximum degree bounded by 4, and 0/1 symmetric costs.
ISSN:0304-3975
1879-2294
DOI:10.1016/j.tcs.2017.06.013