TY - GEN

T1 - The complexity of routing with few collisions

AU - Fluschnik, Till

AU - Morik, Marco

AU - Sorge, Manuel

N1 - Publisher Copyright:
© Springer-Verlag GmbH Germany 2017.

PY - 2017/1/1

Y1 - 2017/1/1

N2 - We study the computational complexity of routing multiple objects through a network in such a way that only few collisions occur: Given a graph G with two distinct terminal vertices and two positive integers p and k, the question is whether one can connect the terminals by at least p routes (e.g. paths) such that at most k edges are time-wise shared among them. We study three types of routes: traverse each vertex at most once (paths), each edge at most once (trails), or no such restrictions (walks). We prove that for paths and trails the problem is NP-complete on undirected and directed graphs even if k is constant or the maximum vertex degree in the input graph is constant. For walks, however, it is solvable in polynomial time on undirected graphs for arbitrary k and on directed graphs if k is constant. We additionally study for all route types a variant of the problem where the maximum length of a route is restricted by some given upper bound. We prove that this length-restricted variant has the same complexity classification with respect to paths and trails, but for walks it becomes NP-complete on undirected graphs.

AB - We study the computational complexity of routing multiple objects through a network in such a way that only few collisions occur: Given a graph G with two distinct terminal vertices and two positive integers p and k, the question is whether one can connect the terminals by at least p routes (e.g. paths) such that at most k edges are time-wise shared among them. We study three types of routes: traverse each vertex at most once (paths), each edge at most once (trails), or no such restrictions (walks). We prove that for paths and trails the problem is NP-complete on undirected and directed graphs even if k is constant or the maximum vertex degree in the input graph is constant. For walks, however, it is solvable in polynomial time on undirected graphs for arbitrary k and on directed graphs if k is constant. We additionally study for all route types a variant of the problem where the maximum length of a route is restricted by some given upper bound. We prove that this length-restricted variant has the same complexity classification with respect to paths and trails, but for walks it becomes NP-complete on undirected graphs.

UR - http://www.scopus.com/inward/record.url?scp=85029407442&partnerID=8YFLogxK

U2 - 10.1007/978-3-662-55751-8_21

DO - 10.1007/978-3-662-55751-8_21

M3 - Conference contribution

AN - SCOPUS:85029407442

SN - 9783662557501

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

SP - 257

EP - 270

BT - Fundamentals of Computation Theory - 21st International Symposium, FCT 2017, Proceedings

A2 - Zeitoun, Marc

A2 - Klasing, Ralf

PB - Springer Verlag

T2 - 21st International Symposium on Fundamentals of Computation Theory, FCT 2017

Y2 - 11 September 2017 through 13 September 2017

ER -