scholarly journals Approximation Algorithms for Edge-Disjoint Paths and Unsplittable Flow

2006 ◽  
pp. 97-134 ◽  
Author(s):  
Thomas Erlebach
Keyword(s):  
Approximation Algorithms ◽  
Disjoint Paths ◽  
Edge Disjoint ◽  
Unsplittable Flow

scholarly journals Near-optimal hardness results and approximation algorithms for edge-disjoint paths and related problems

2003 ◽  
Vol 67 (3) ◽  
pp. 473-496 ◽  
Author(s):  
Venkatesan Guruswami ◽  
Sanjeev Khanna ◽  
Rajmohan Rajaraman ◽  
Bruce Shepherd ◽  
Mihalis Yannakakis
Keyword(s):  
Approximation Algorithms ◽  
Disjoint Paths ◽  
Edge Disjoint

scholarly journals On Structural Parameterizations of the Edge Disjoint Paths Problem

Algorithmica ◽  
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.

Sign in / Sign up

Export Citation Format

Share Document