TY - GEN

T1 - The minimum shared edges problem on grid-like graphs

AU - Fluschnik, Till

AU - Hatzel, Meike

AU - Härtlein, Steffen

AU - Molter, Hendrik

AU - Seidler, Henning

N1 - Funding Information:
A full version is available at https://arxiv.org/abs/1703.02332. T. Fluschnik—Supported by the DFG, project DAMM (NI 369/13-2). H. Molter—Partially supported by the DFG, project DAPA (NI 369/12).
Publisher Copyright:
© 2017, Springer International Publishing AG.

PY - 2017/1/1

Y1 - 2017/1/1

N2 - 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 (i.e. finite) 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 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.

AB - 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 (i.e. finite) 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 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.

UR - http://www.scopus.com/inward/record.url?scp=85034046487&partnerID=8YFLogxK

U2 - 10.1007/978-3-319-68705-6_19

DO - 10.1007/978-3-319-68705-6_19

M3 - Conference contribution

AN - SCOPUS:85034046487

SN - 9783319687049

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 249

EP - 262

BT - Graph-Theoretic Concepts in Computer Science - 43rd International Workshop, WG 2017, Revised Selected Papers

A2 - Woeginger, Gerhard J.

A2 - Bodlaender, Hans L.

PB - Springer Verlag

T2 - 43rd International Workshop on Graph-Theoretic Concepts in Computer Science, WG 2017

Y2 - 21 June 2017 through 23 June 2017

ER -