An Improved FPT Algorithm for Independent Feedback Vertex Set

Li, Shaohua; Pilipczuk, Marcin

doi:10.1007/s00224-020-09973-w

Cited by 6 publications

(3 citation statements)

References 25 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…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%

See 1 more Smart Citation

Improved FPT Algorithms for Deletion to Forest-like Structures

Gowda,

Lonkar,

Panolan

et al. 2020

Preprint

View full text Add to dashboard Cite

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 }).

show abstract

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

View full text Add to dashboard Cite

show abstract

“…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

View full text Add to dashboard Cite

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.

show abstract