The Power of Cut-Based Parameters for Computing Edge-Disjoint Paths

This paper revisits 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 aim is to identify structural properties (parameters...

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Bibliographic Details
Published in:Algorithmica Vol. 83; no. 2; pp. 726 - 752
Main Authors: Ganian, Robert, Ordyniak, Sebastian
Format: Journal Article
Language:English
Published: New York Springer US 01.02.2021
Springer Nature B.V
Subjects:
Algorithm Analysis and Problem Complexity
Algorithms
Computer Science
Computer Systems Organization and Communication Networks
Cut width
Data Structures and Information Theory
Graphs
Mathematics of Computing
Parameter identification
Parameterization
Polynomials
Separators
Theory of Computation
Edge-disjoint path problem
Tree-cut width
Feedback edge set
Parameterized complexity
ISSN:0178-4617, 1432-0541
Online Access:Get full text
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Summary:This paper revisits 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 aim is to identify structural properties (parameters) of graphs which allow the efficient solution of EDP without restricting the placement of terminals in P in any way. In this setting, EDP is known to remain NP-hard even on extremely restricted graph classes, such as graphs with a vertex cover of size 3. We present three results which use edge-separator based parameters to chart new islands of tractability in the complexity landscape of EDP. Our first and main result utilizes the fairly recent structural parameter tree-cut width (a parameter with fundamental ties to graph immersions and graph cuts): we obtain a polynomial-time algorithm for EDP on every graph class of bounded tree-cut width. Our second result shows that EDP parameterized by tree-cut width is unlikely to be fixed-parameter tractable. Our final, third result is a polynomial kernel for EDP parameterized by the size of a minimum feedback edge set in the graph.
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ISSN:0178-4617
1432-0541
DOI:10.1007/s00453-020-00772-w