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

Given a graph \(G=(V,E)\), two vertices \(s,t\in V\), and two integers \(k,\ell\), the Short Secluded Path problem is to find a simple \(s\)-\(t\)-path with at most \(k\) vertices and \(\ell\) neighbors. We study the parameterized complexity of the problem with respect to four structural graph param...

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Veröffentlicht in:arXiv.org 2019-06
Hauptverfasser: René van Bevern, Fluschnik, Till, Oxana Yu Tsidulko
Format: Artikel
Sprache:eng
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Zusammenfassung:Given a graph \(G=(V,E)\), two vertices \(s,t\in V\), and two integers \(k,\ell\), the Short Secluded Path problem is to find a simple \(s\)-\(t\)-path with at most \(k\) vertices and \(\ell\) 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 \(\ell\). We also obtain a \(2^{O(w)}\cdot \ell^2\cdot n\)-time algorithm for graphs of treewidth \(w\), which yields subexponential-time algorithms in several graph classes.
ISSN:2331-8422
DOI:10.48550/arxiv.1806.09540