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 - 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 -