eng
Schloss Dagstuhl β Leibniz-Zentrum fΓΌr Informatik
Leibniz International Proceedings in Informatics
1868-8969
2020-12-04
34:1
34:16
10.4230/LIPIcs.ISAAC.2020.34
article
Improved FPT Algorithms for Deletion to Forest-Like Structures
Gowda, Kishen N.
1
Lonkar, Aditya
2
Panolan, Fahad
3
Patel, Vraj
1
Saurabh, Saket
4
IIT Gandhinagar, India
IIT Madras, India
Department of Computer Science and Engineering, IIT Hyderabad, India
Institute of Mathematical Sciences, Chennai, India
The Feedback Vertex Set problem is undoubtedly one of the most well-studied problems in Parameterized Complexity. In this problem, given an undirected graph G and a non-negative integer k, the objective is to test whether there exists a subset S β V(G) of size at most k such that G-S is a forest. After a long line of improvement, recently, Li and Nederlof [SODA, 2020] designed a randomized algorithm for the problem running in time πͺ^β(2.7^k). In the Parameterized Complexity literature, several problems around Feedback Vertex Set have been studied. Some of these include Independent Feedback Vertex Set (where the set S should be an independent set in G), Almost Forest Deletion and Pseudoforest Deletion. In Pseudoforest Deletion, each connected component in G-S has at most one cycle in it. However, in Almost Forest Deletion, the input is a graph G and non-negative integers k,π β β, and the objective is to test whether there exists a vertex subset S of size at most k, such that G-S is π edges away from a forest. In this paper, using the methodology of Li and Nederlof [SODA, 2020], we obtain the current fastest algorithms for all these problems. In particular we obtain following randomized algorithms.
1) Independent Feedback Vertex Set can be solved in time πͺ^β(2.7^k).
2) Pseudo Forest Deletion can be solved in time πͺ^β(2.85^k).
3) Almost Forest Deletion can be solved in πͺ^β(min{2.85^k β
8.54^π, 2.7^k β
36.61^π, 3^k β
1.78^π}).
https://drops.dagstuhl.de/storage/00lipics/lipics-vol181-isaac2020/LIPIcs.ISAAC.2020.34/LIPIcs.ISAAC.2020.34.pdf
Parameterized Complexity
Independent Feedback Vertex Set
PseudoForest
Almost Forest
Cut and Count
Treewidth