Parameterized complexity of the MINCCA problem on graphs of bounded decomposability

Abstract

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.