A Polynomial Kernel for Distance-Hereditary Vertex Deletion

Kim, Eun Jung; Kwon, O-joung

doi:10.1007/s00453-021-00820-z

Cited by 7 publications

(6 citation statements)

References 27 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Jansen and Pilipczuk [20] presented a kernel with Opk 161 log 58 kq vertices for Chordal Deletion, and Agrawal et al [2] improved this result by presenting a kernel with Opk 12 log 10 kq vertices. Kim and Kwon [21] presented a kernel with Opk 30 log 5 kq vertices for Distancehereditary Deletion. This leads us to the main result of our paper: Theorem 1.2.…”

Section: -Leaf Power Deletionmentioning

confidence: 99%

A polynomial kernel for $3$-leaf power deletion

Ahn¹,

Eiben²,

Kwon³

et al. 2019

Preprint

Self Cite

View full text Add to dashboard Cite

A graph G is an ℓ-leaf power of a tree T if V pGq is equal to the set of leaves of T , and distinct vertices v and w of G are adjacent if and only if the distance between v and w in T is at most ℓ. Given a graph G, 3-leaf Power Deletion asks whether there is a set S Ď V pGq of size at most k such that GzS is a 3-leaf power of some tree T . We provide a polynomial kernel for this problem. More specifically, we present a polynomial-time algorithm for an input instance pG, kq to output an equivalent instance pG 1 , k 1 q such that k 1 ď k and G 1 has at most Opk 14 log 12 kq vertices.

show abstract

Section: -Leaf Power Deletionmentioning

confidence: 99%

A polynomial kernel for $3$-leaf power deletion

Ahn¹,

Eiben²,

Kwon³

et al. 2019

Preprint

Self Cite

View full text Add to dashboard Cite

show abstract

“…There is a large body of work in the theory of parameterized complexity, where F-Deletion for many F's is shown to be in FPT or even admits a polynomial kernel. The list of such F's includes chordal graphs [24,17,3], interval graphs [8,7,4], distance-hereditary graphs [11,19], bipartite graphs [26,22], and graphs with bounded treewidth [14,21].…”

Section: Introductionmentioning

confidence: 99%

Towards Constant-Factor Approximation for Chordal/Distance-Hereditary Vertex Deletion

2022

Self Cite

View full text Add to dashboard Cite

For a family of graphs F, Weighted F-Deletion is the problem for which the input is a vertex weighted graph G " pV, Eq and the goal is to delete S Ď V with minimum weight such that GzS P F. Designing a constant-factor approximation algorithm for large subclasses of perfect graphs has been an interesting research direction. Block graphs, 3-leaf power graphs, and interval graphs are known to admit constant-factor approximation algorithms, but the question is open for chordal graphs and distance-hereditary graphs.In this paper, we add one more class to this list by presenting a constant-factor approximation algorithm when F is the intersection of chordal graphs and distance-hereditary graphs. They are known as ptolemaic graphs and form a superset of both block graphs and 3-leaf power graphs above. Our proof presents new properties and algorithmic results on inter-clique digraphs as well as an approximation algorithm for a variant of Feedback Vertex Set that exploits this relationship (named Feedback Vertex Set with Precedence Constraints), each of which may be of independent interest. ACM Subject ClassificationTheory of computation Ñ Design and analysis of algorithms; Theory of computation Ñ Graph algorithms analysis

show abstract

“…There is a large body of work in the theory of parameterized complexity, where F-Deletion for many F's is shown to be in FPT or even admits a polynomial kernel. The list of such F's includes chordal graphs [26,19,2], interval graphs [8,7,4], distance-hereditary graphs [12,21], bipartite graphs [28,24], and graphs with bounded treewidth [15,23].…”

Section: Introductionmentioning

confidence: 99%

“…It is supposedly the simplest dense graph class captured by a graph width parameter; distance-hereditary graphs are precisely the graphs of rankwidth 1 [27]. F-Deletion for distance-hereditary graphs has gained good attention for fixed-parameter tractability and approximability [3,21,12] particularly due to the recent surge of interest in rankwidth. An Oplog 3 nq-approximation is known [3].…”

Section: Introductionmentioning

confidence: 99%

Towards constant-factor approximation for chordal / distance-hereditary vertex deletion

Ahn¹,

Kim²,

Lee³

2020

Preprint

Self Cite

View full text Add to dashboard Cite

For a family of graphs F, Weighted F-Deletion is the problem for which the input is a vertex weighted graph G " pV, Eq and the goal is to delete S Ď V with minimum weight such that GzS P F. Designing a constant-factor approximation algorithm for large subclasses of perfect graphs has been an interesting research direction. Block graphs, 3leaf power graphs, and interval graphs are known to admit constant-factor approximation algorithms, but the question is open for chordal graphs and distance-hereditary graphs.In this paper, we add one more class to this list by presenting a constant-factor approximation algorithm when F is the intersection of chordal graphs and distancehereditary graphs. They are known as ptolemaic graphs and form a superset of both block graphs and 3-leaf power graphs above. Our proof presents new properties and algorithmic results on inter-clique digraphs as well as an approximation algorithm for a variant of Feedback Vertex Set that exploits this relationship (named Feedback Vertex Set with Precedence Constraints), each of which may be of independent interest.

show abstract

A Polynomial Kernel for Distance-Hereditary Vertex Deletion

Cited by 7 publications

References 27 publications

A polynomial kernel for $3$-leaf power deletion

A polynomial kernel for $3$-leaf power deletion

Towards Constant-Factor Approximation for Chordal/Distance-Hereditary Vertex Deletion

Towards constant-factor approximation for chordal / distance-hereditary vertex deletion

Contact Info

Product

Resources

About