The Minimum Shared Edges Problem on Grid-Like Graphs [chapter]

Till Fluschnik, Meike Hatzel, Steffen Härtlein, Hendrik Molter, Henning Seidler
2017 Lecture Notes in Computer Science  
We study the NP-hard Minimum Shared Edges (MSE) problem on graphs: decide whether it is possible to route p paths from a start vertex to a target vertex in a given graph while using at most k edges more than once. We show that MSE can be decided on bounded grids in linear time when both dimensions are either small or large compared to the number p of paths. On the contrary, we show that MSE remains NP-hard on subgraphs of bounded grids. Finally, we study MSE from a parametrised complexity point
more » ... of view. It is known that MSE is fixed-parameter tractable with respect to the number p of paths. We show that, under standard complexity-theoretical assumptions, the problem parametrised by the combined parameter k, p, maximum degree, diameter, and treewidth does not admit a polynomial-size problem kernel, even when restricted to planar graphs. * Supported by the DFG, project DAMM (NI 369/13-2). † Partially supported by the DFG, project DAPA (NI 369/12).
doi:10.1007/978-3-319-68705-6_19 fatcat:ia7r2s2zy5gtla342gxsyehqr4