eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2023-08-21
62:1
62:15
10.4230/LIPIcs.MFCS.2023.62
article
Parameterized Max Min Feedback Vertex Set
Lampis, Michael
1
https://orcid.org/0000-0002-5791-0887
Melissinos, Nikolaos
2
https://orcid.org/0000-0002-0864-9803
Vasilakis, Manolis
1
https://orcid.org/0000-0001-6505-2977
Université Paris-Dauphine, PSL University, CNRS, LAMSADE, 75016, Paris, France
Department of Theoretical Computer Science, Faculty of Information Technology, Czech Technical University in Prague, Czech Republic
Given a graph G and an integer k, Max Min FVS asks whether there exists a minimal set of vertices of size at least k whose deletion destroys all cycles. We present several results that improve upon the state of the art of the parameterized complexity of this problem with respect to both structural and natural parameters.
Using standard DP techniques, we first present an algorithm of time tw^O(tw) n^O(1), significantly generalizing a recent algorithm of Gaikwad et al. of time vc^O(vc) n^O(1), where tw, vc denote the input graph’s treewidth and vertex cover respectively. Subsequently, we show that both of these algorithms are essentially optimal, since a vc^o(vc) n^O(1) algorithm would refute the ETH.
With respect to the natural parameter k, the aforementioned recent work by Gaikwad et al. claimed an FPT branching algorithm with complexity 10^k n^O(1). We point out that this algorithm is incorrect and present a branching algorithm of complexity 9.34^k n^O(1).
https://drops.dagstuhl.de/storage/00lipics/lipics-vol272-mfcs2023/LIPIcs.MFCS.2023.62/LIPIcs.MFCS.2023.62.pdf
ETH
Feedback vertex set
Parameterized algorithms
Treewidth