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Improved FPT Algorithms for Deletion to Forest-Like Structures Gowda, Kishen N. Lonkar, Aditya Panolan, Fahad Patel, Vraj Saurabh, Saket Parameterized Complexity Independent Feedback Vertex Set PseudoForest Almost Forest Cut and Count Treewidth 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 ⊆ 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 𝒪^⋆(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,𝓁 ∈ ℕ, and the objective is to test whether there exists a vertex subset S of size at most k, such that G-S is 𝓁 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 𝒪^⋆(2.7^k). 2) Pseudo Forest Deletion can be solved in time 𝒪^⋆(2.85^k). 3) Almost Forest Deletion can be solved in 𝒪^⋆(min{2.85^k ⋅ 8.54^𝓁, 2.7^k ⋅ 36.61^𝓁, 3^k ⋅ 1.78^𝓁}). Schloss Dagstuhl – Leibniz-Zentrum für Informatik Kishen N. Gowda and Aditya Lonkar and Fahad Panolan and Vraj Patel and Saket Saurabh 2020 Is Part Of LIPIcs, Volume 181, 31st International Symposium on Algorithms and Computation (ISAAC 2020) InProceedings Text doc-type:ResearchArticle publishedVersion application/pdf doi:10.4230/LIPIcs.ISAAC.2020.34 urn:nbn:de:0030-drops-133781 https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ISAAC.2020.34 eng https://creativecommons.org/licenses/by/3.0/legalcode