Parameterized complexity of lengthbounded cuts and multicuts
Abstract
We show that the Minimal LengthBounded LBut problem can be computed in linear time with respect to L and the treewidth of the input graph as parameters. In this problem the task is to find a set of edges of a graph such that after removal of this set, the shortest path between two prescribed vertices is at least L long. We derive an FPT algorithm for a more general multicommodity length bounded cut problem when parameterized by the number of terminals also. For the former problem we show a W[1]hardness result when the parameterization is done by the pathwidth only (instead of the treewidth) and that this problem does not admit polynomial kernel when parameterized by treewidth and L. We also derive an FPT algorithm for the Minimal LengthBounded Cut problem when parameterized by the treedepth. Thus showing an interesting paradigm for this problem and parameters treedepth and pathwidth.
 Publication:

arXiv eprints
 Pub Date:
 November 2015
 arXiv:
 arXiv:1511.02801
 Bibcode:
 2015arXiv151102801K
 Keywords:

 Computer Science  Data Structures and Algorithms;
 05C21;
 05C85;
 F.2.2;
 G.2.2
 EPrint:
 20 pages, 7 figures, TAMC 2015 proceedings