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When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.ISAAC.2020.34
URN: urn:nbn:de:0030-drops-133781
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2020/13378/
Gowda, Kishen N. ;
Lonkar, Aditya ;
Panolan, Fahad ;
Patel, Vraj ;
Saurabh, Saket
Improved FPT Algorithms for Deletion to Forest-Like Structures
Abstract
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 ?^⋆(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,? ∈ ℕ, and the objective is to test whether there exists a vertex subset S of size at most k, such that G-S is ? 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 ?^⋆(2.7^k).
2) Pseudo Forest Deletion can be solved in time ?^⋆(2.85^k).
3) Almost Forest Deletion can be solved in ?^⋆(min{2.85^k ⋅ 8.54^?, 2.7^k ⋅ 36.61^?, 3^k ⋅ 1.78^?}).
BibTeX - Entry
@InProceedings{gowda_et_al:LIPIcs:2020:13378,
author = {Kishen N. Gowda and Aditya Lonkar and Fahad Panolan and Vraj Patel and Saket Saurabh},
title = {{Improved FPT Algorithms for Deletion to Forest-Like Structures}},
booktitle = {31st International Symposium on Algorithms and Computation (ISAAC 2020)},
pages = {34:1--34:16},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-173-3},
ISSN = {1868-8969},
year = {2020},
volume = {181},
editor = {Yixin Cao and Siu-Wing Cheng and Minming Li},
publisher = {Schloss Dagstuhl--Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/opus/volltexte/2020/13378},
URN = {urn:nbn:de:0030-drops-133781},
doi = {10.4230/LIPIcs.ISAAC.2020.34},
annote = {Keywords: Parameterized Complexity, Independent Feedback Vertex Set, PseudoForest, Almost Forest, Cut and Count, Treewidth}
}
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Keywords: |
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Parameterized Complexity, Independent Feedback Vertex Set, PseudoForest, Almost Forest, Cut and Count, Treewidth |
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Collection: |
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31st International Symposium on Algorithms and Computation (ISAAC 2020) |
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Issue Date: |
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2020 |
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Date of publication: |
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04.12.2020 |
