An Improved FPT Algorithm for Independent Feedback Vertex Set

Li, Shaohua; Pilipczuk, Marcin

doi:10.1007/s00224-020-09973-w

Cited by 5 publications

(3 citation statements)

References 25 publications

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“…On the other hand setting = 0 in Almost Forest Deletion results in FVS. The best known algorithms for Independent FVS, Almost Forest Deletion, and Pseudoforest Deletion are O (3.619 k ) [24], O (5 k 4 ) [25], and O (3 k ) [5], respectively. Our main objective is to improve over these running times for the corresponding problems.…”

Section: Our Problems Results and Methodsmentioning

confidence: 99%

“…However, just in last few months both these algorithms have been improved; Iwata and Kobayashi [16, IPEC 2019] designed the fastest known deterministic algorithm with running time O (3.460 k ) and Li and Nederlof [23, SODA 2020] designed the fastest known randomized algorithm with running time O (2.7 k ). The success on FVS has led to the study of many variants of FVS in literature such as Connected FVS [9,28], Independent FVS [1,24,27], Simultaneous FVS [2,33], Subset FVS [11,17,18,19,26], Pseudoforest Deletion [5,30], Generalized Pseudoforest Deletion [30], and Almost Forest Deletion [31,25].…”

Section: Introductionmentioning

confidence: 99%

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Improved FPT Algorithms for Deletion to Forest-like Structures

Gowda,

Lonkar,

Panolan

et al. 2020

Preprint

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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 ) 1 . 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 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 , 2.7 k • 36.61 , 3 k • 1.78 }).

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Section: Our Problems Results and Methodsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Improved FPT Algorithms for Deletion to Forest-like Structures

Gowda,

Lonkar,

Panolan

et al. 2020

Preprint

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“…The parameterized complexity of corresponding problems Connected Feedback Vertex Set, Independent Feedback Vertex Set, and Tree Deletion Set was studied in [11,17,19,20,23].…”

Section: Applicationsmentioning

confidence: 99%

Maintaining $\mathsf{CMSO}_2$ properties on dynamic structures with bounded feedback vertex number

Majewski¹,

Pilipczuk²,

Sokołowski³

2021

Preprint

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Let ϕ be a sentence of CMSO 2 (monadic second-order logic with quantification over edge subsets and counting modular predicates) over the signature of graphs. We present a dynamic data structure that for a given graph G that is updated by edge insertions and edge deletions, maintains whether ϕ is satisfied in G. The data structure is required to correctly report the outcome only when the feedback vertex number of G does not exceed a fixed constant k, otherwise it reports that the feedback vertex number is too large. With this assumption, we guarantee amortized update time O ϕ,k (log n).By combining this result with a classic theorem of Erdős and Pósa, we give a fully dynamic data structure that maintains whether a graph contains a packing of k vertexdisjoint cycles with amortized update time O k (log n). Our data structure also works in a larger generality of relational structures over binary signatures.

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