Edge-Disjoint Branchings in Temporal Graphs

Lecture Notes in Computer Science - Combinatorial Algorithms ◽

10.1007/978-3-030-48966-3_9 ◽

2020 ◽

pp. 112-125 ◽

Cited By ~ 1

Author(s):

Victor Campos ◽

Raul Lopes ◽

Andrea Marino ◽

Ana Silva

Keyword(s):

Edge Disjoint ◽

Temporal Graphs

Download Full-text

Mixed metric dimension of graphs with edge disjoint cycles

Discrete Applied Mathematics ◽

10.1016/j.dam.2021.05.004 ◽

2021 ◽

Vol 300 ◽

pp. 1-8

Author(s):

Jelena Sedlar ◽

Riste Škrekovski

Keyword(s):

Metric Dimension ◽

Edge Disjoint ◽

Disjoint Cycles ◽

Mixed Metric

Download Full-text

Solving the Maximum Edge Disjoint Path Problem Using a Modified Lagrangian Particle Swarm Optimisation Hybrid

European Journal of Operational Research ◽

10.1016/j.ejor.2021.01.009 ◽

2021 ◽

Author(s):

Jake Weiner ◽

Andreas T. Ernst ◽

Xiaodong Li ◽

Yuan Sun ◽

Kalyanmoy Deb

Keyword(s):

Particle Swarm ◽

Particle Swarm Optimisation ◽

Disjoint Path ◽

Lagrangian Particle ◽

Edge Disjoint ◽

Edge Disjoint Path

Download Full-text

On Structural Parameterizations of the Edge Disjoint Paths Problem

Algorithmica ◽

10.1007/s00453-020-00795-3 ◽

2021 ◽

Author(s):

Robert Ganian ◽

Sebastian Ordyniak ◽

M. S. Ramanujan

Keyword(s):

Polynomial Time ◽

Disjoint Paths ◽

Structural Parameter ◽

Input Graph ◽

Feedback Vertex Set ◽

Fpt Algorithms ◽

Edge Disjoint ◽

Fpt Algorithm ◽

Vertex Set ◽

Terminal Pair

AbstractIn 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 -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 [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.

Download Full-text