R. Ganian, S. Ordyniak, M. Ramanujan:

"On Structural Parameterizations of the Edge Disjoint Paths Problem";

Algorithmica,83(2021), 1605 - 1637.

In this paper we revisit the classical edge disjoint paths (EDP) problem, where one

is given an undirected graph G and a set of terminal pairs P and asks whether G

contains a set of pairwise edge-disjoint paths connecting every terminal pair in P.

Our focus lies on structural parameterizations for the problem that allow for efficient

(polynomial-time or FPT) algorithms. As our first result, we answer an open

question stated in Fleszar et al. (Proceedings of the ESA, 2016), by showing that

the problem can be solved in polynomial time if the input graph has a feedback vertex

set of size one. We also show that EDP parameterized by the treewidth and the

maximum degree of the input graph is fixed-parameter tractable. Having developed

two novel algorithms for EDP using structural restrictions on the input graph, we

then turn our attention towards the augmented graph, i.e., the graph obtained from

the input graph after adding one edge between every terminal pair. In constrast to

the input graph, where EDP is known to remain NP-hard even for treewidth two, a

result by Zhou et al. (Algorithmica 26(1):3--30, 2000) shows that EDP can be solved

in non-uniform polynomial time if the augmented graph has constant treewidth; we

note that the possible improvement of this result to an FPT-algorithm has remained

open since then. We show that this is highly unlikely by establishing the W[1]-hardness

of the problem parameterized by the treewidth (and even feedback vertex set)

of the augmented graph. Finally, we develop an FPT-algorithm for EDP by exploiting

a novel structural parameter of the augmented graph.

http://dx.doi.org/10.1007/s00453-020-00795-3

https://publik.tuwien.ac.at/files/publik_300152.pdf

Created from the Publication Database of the Vienna University of Technology.