Parameterized algorithms and data reduction for the short secluded s‐t‐path problem

Given a graph G = (V, E), two vertices s, t ∈ V, and two integers k, ℓ, the Short Secluded Path problem is to find a simple s‐t‐path with at most k vertices and ℓ neighbors. We study the parameterized complexity of the problem with respect to four structural graph parameters: the vertex cover number...

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Bibliographic Details
Published in:Networks Vol. 75; no. 1; pp. 34 - 63
Main Authors: Bevern, René, Fluschnik, Till, Tsidulko, Oxana Yu
Format: Journal Article
Language:English
Published: Hoboken, USA John Wiley & Sons, Inc 01.01.2020
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Subjects:
Algorithms
Apexes
Data reduction
Feedback
fixed‐parameter tractability
Graph theory
kernelization lower bounds
NP‐hard problem
Parameterization
Parameters
Polynomials
problem kernelization
subexponential time
treewidth
ISSN:0028-3045, 1097-0037
Online Access:Get full text
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Summary:Given a graph G = (V, E), two vertices s, t ∈ V, and two integers k, ℓ, the Short Secluded Path problem is to find a simple s‐t‐path with at most k vertices and ℓ neighbors. We study the parameterized complexity of the problem with respect to four structural graph parameters: the vertex cover number, treewidth, feedback vertex number, and feedback edge number. In particular, we completely settle the question of the existence of problem kernels with size polynomial in these parameters and their combinations with k and ℓ. We also obtain a 2O(tw) · ℓ2 · n‐time algorithm for n‐vertex graphs of treewidth tw, which yields subexponential‐time algorithms in several graph classes.
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ISSN:0028-3045
1097-0037
DOI:10.1002/net.21904