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

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2 Citations (Scopus)

Abstract

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.

Original languageEnglish
Pages (from-to)34-63
Number of pages30
JournalNetworks
Volume75
Issue number1
DOIs
Publication statusPublished - Jan 2020

Keywords

  • fixed-parameter tractability
  • kernelization lower bounds
  • NP-hard problem
  • problem kernelization
  • subexponential time
  • treewidth
  • EULERIAN EXTENSION
  • APPROXIMATION
  • COMPLEXITY

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