Faster Exact and Parameterized Algorithm for Feedback Vertex Set in Tournaments

Kumar, Mithilesh; Lokshtanov, Daniel

doi:10.4230/lipics.stacs.2016.49

Cited by 2 publications

(1 citation statement)

References 10 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Fomin et al [26] showed that Cluster Vertex Deletion and Directed FVS in Tournaments admit subquadratic kernels with O(k 5/3 ) vertices and O(k 3/2 ) vertices, while the size of the best kernel for SFVS in Chordal Graphs is still quadratic, which can be easily obtained from the kernelization for 3-Hitting Set [24]. As for parameterized algorithms, Dom et al [27] first designed an O * (2 k )-time algorithm for Directed FVS in Tournaments, breaking the barrier of 3-Hitting Set, and the running time bound of which was later improved to O * (1.619 k ) by Kumar and Lokshtanov [28]. In 2010, Hüffne et al [29] first broke the barrier of 3-Hitting Set by obtaining an O * (2 k )-time algorithm for Cluster Vertex Deletion.…”

Section: Introductionmentioning

confidence: 99%

Breaking the Barrier 2k for Subset Feedback Vertex Set in Chordal Graphs

Bai

Xiao

2022

Preprint

View full text Add to dashboard Cite

The Subset Feedback Vertex Set problem (SFVS), to delete $k$ vertices from a given graph such that any vertex in a vertex subset (called a terminal set) is not in a cycle in the remaining graph, generalizes the famous Feedback Vertex Set problem and Multiway Cut problem. SFVS remains $|NP|$-hard even in split and chordal graphs, and SFVS in Chordal Graphs can be considered as a special case of the 3-Hitting Set problem. However, it is not easy to solve SFVS in Chordal Graphs faster than 3-Hitting Set. In 2019, Philip, Rajan, Saurabh, and Tale (Algorithmica 2019) proved that SFVS in Chordal Graphs can be solved in $2^{k}n^{\mathcal{O}(1)}$ time, slightly improving the best result $2.076^{k}n^{\mathcal{O}(1)}$ for 3-Hitting Set. In this paper, we break the ``$2^{k}$-barrier'' for SFVS in Chordal Graphs by giving a $1.619^{k}n^{\mathcal{O}(1)}$-time algorithm. Our algorithm uses reduction and branching rules based on the Dulmage-Mendelsohn decomposition and a divide-and-conquer method.

show abstract