A faster FPT algorithm and a smaller kernel for block graph vertex deletion

Akanksha Agrawal; Sudeshna Kolay; Daniel Lokshtanov; Saket Saurabh

doi:10.1007/978-3-662-49529-2_1

A faster FPT algorithm and a smaller kernel for block graph vertex deletion

Akanksha Agrawal, Sudeshna Kolay, Daniel Lokshtanov, Saket Saurabh

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

26 Scopus citations

Abstract

A graph G is called a block graph if every maximal 2-connected component of G is a clique. In this paper we study the Block Graph Vertex Deletion from the perspective of fixed parameter tractable (FPT) and kernelization algorithms. In particular, an input to Block Graph Vertex Deletion consists of a graph G and a positive integer k, and the objective to check whether there exists a subset S ⊆ V (G) of size at most k such that the graph induced on V (G)\S is a block graph. In this paper we give an FPT algorithm with running time 4^kn^O(1) and a polynomial kernel of size O(k⁴) for Block Graph Vertex Deletion. The running time of our FPT algorithm improves over the previous best algorithm for the problem that runs in time 10^kn^O(1), and the size of our kernel reduces over the previously known kernel of size O(k⁶). Our results are based on a novel connection between Block Graph Vertex Deletion and the classical Feedback Vertex Set problem in graphs without induced C⁴ and K⁴ − e. To achieve our results we also obtain an algorithm for Weighted Feedback Vertex Set running in time 3.618^kn^O(1) and improving over the running time of previously known algorithm with running time 5^kn^O(1).

Original language	English
Title of host publication	LATIN 2016
Subtitle of host publication	Theoretical Informatics - 12th Latin American Symposium, Proceedings
Editors	Gonzalo Navarro, Evangelos Kranakis, Edgar Chávez
Publisher	Springer Verlag
Pages	1-13
Number of pages	13
ISBN (Print)	9783662495285
DOIs	https://doi.org/10.1007/978-3-662-49529-2_1
State	Published - 1 Jan 2016
Externally published	Yes
Event	12th Latin American Symposium on Theoretical Informatics, LATIN 2016 - Ensenada, Mexico Duration: 11 Apr 2016 → 15 Apr 2016

Publication series

Name	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume	9644
ISSN (Print)	0302-9743
ISSN (Electronic)	1611-3349

Conference

Conference	12th Latin American Symposium on Theoretical Informatics, LATIN 2016
Country/Territory	Mexico
City	Ensenada
Period	11/04/16 → 15/04/16

ASJC Scopus subject areas

Theoretical Computer Science
General Computer Science

Access to Document

10.1007/978-3-662-49529-2_1

Cite this

Agrawal, A., Kolay, S., Lokshtanov, D., & Saurabh, S. (2016). A faster FPT algorithm and a smaller kernel for block graph vertex deletion. In G. Navarro, E. Kranakis, & E. Chávez (Eds.), LATIN 2016: Theoretical Informatics - 12th Latin American Symposium, Proceedings (pp. 1-13). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 9644). Springer Verlag. https://doi.org/10.1007/978-3-662-49529-2_1

Agrawal, Akanksha ; Kolay, Sudeshna ; Lokshtanov, Daniel et al. / A faster FPT algorithm and a smaller kernel for block graph vertex deletion. LATIN 2016: Theoretical Informatics - 12th Latin American Symposium, Proceedings. editor / Gonzalo Navarro ; Evangelos Kranakis ; Edgar Chávez. Springer Verlag, 2016. pp. 1-13 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).

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abstract = "A graph G is called a block graph if every maximal 2-connected component of G is a clique. In this paper we study the Block Graph Vertex Deletion from the perspective of fixed parameter tractable (FPT) and kernelization algorithms. In particular, an input to Block Graph Vertex Deletion consists of a graph G and a positive integer k, and the objective to check whether there exists a subset S ⊆ V (G) of size at most k such that the graph induced on V (G)\S is a block graph. In this paper we give an FPT algorithm with running time 4knO(1) and a polynomial kernel of size O(k4) for Block Graph Vertex Deletion. The running time of our FPT algorithm improves over the previous best algorithm for the problem that runs in time 10knO(1), and the size of our kernel reduces over the previously known kernel of size O(k6). Our results are based on a novel connection between Block Graph Vertex Deletion and the classical Feedback Vertex Set problem in graphs without induced C4 and K4 − e. To achieve our results we also obtain an algorithm for Weighted Feedback Vertex Set running in time 3.618knO(1) and improving over the running time of previously known algorithm with running time 5knO(1).",

author = "Akanksha Agrawal and Sudeshna Kolay and Daniel Lokshtanov and Saket Saurabh",

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Agrawal, A, Kolay, S, Lokshtanov, D & Saurabh, S 2016, A faster FPT algorithm and a smaller kernel for block graph vertex deletion. in G Navarro, E Kranakis & E Chávez (eds), LATIN 2016: Theoretical Informatics - 12th Latin American Symposium, Proceedings. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 9644, Springer Verlag, pp. 1-13, 12th Latin American Symposium on Theoretical Informatics, LATIN 2016, Ensenada, Mexico, 11/04/16. https://doi.org/10.1007/978-3-662-49529-2_1

A faster FPT algorithm and a smaller kernel for block graph vertex deletion. / Agrawal, Akanksha; Kolay, Sudeshna; Lokshtanov, Daniel et al.
LATIN 2016: Theoretical Informatics - 12th Latin American Symposium, Proceedings. ed. / Gonzalo Navarro; Evangelos Kranakis; Edgar Chávez. Springer Verlag, 2016. p. 1-13 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 9644).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

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AU - Agrawal, Akanksha

AU - Kolay, Sudeshna

AU - Lokshtanov, Daniel

AU - Saurabh, Saket

N1 - Publisher Copyright: © Springer-Verlag Berlin Heidelberg 2016.

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Y1 - 2016/1/1

N2 - A graph G is called a block graph if every maximal 2-connected component of G is a clique. In this paper we study the Block Graph Vertex Deletion from the perspective of fixed parameter tractable (FPT) and kernelization algorithms. In particular, an input to Block Graph Vertex Deletion consists of a graph G and a positive integer k, and the objective to check whether there exists a subset S ⊆ V (G) of size at most k such that the graph induced on V (G)\S is a block graph. In this paper we give an FPT algorithm with running time 4knO(1) and a polynomial kernel of size O(k4) for Block Graph Vertex Deletion. The running time of our FPT algorithm improves over the previous best algorithm for the problem that runs in time 10knO(1), and the size of our kernel reduces over the previously known kernel of size O(k6). Our results are based on a novel connection between Block Graph Vertex Deletion and the classical Feedback Vertex Set problem in graphs without induced C4 and K4 − e. To achieve our results we also obtain an algorithm for Weighted Feedback Vertex Set running in time 3.618knO(1) and improving over the running time of previously known algorithm with running time 5knO(1).

AB - A graph G is called a block graph if every maximal 2-connected component of G is a clique. In this paper we study the Block Graph Vertex Deletion from the perspective of fixed parameter tractable (FPT) and kernelization algorithms. In particular, an input to Block Graph Vertex Deletion consists of a graph G and a positive integer k, and the objective to check whether there exists a subset S ⊆ V (G) of size at most k such that the graph induced on V (G)\S is a block graph. In this paper we give an FPT algorithm with running time 4knO(1) and a polynomial kernel of size O(k4) for Block Graph Vertex Deletion. The running time of our FPT algorithm improves over the previous best algorithm for the problem that runs in time 10knO(1), and the size of our kernel reduces over the previously known kernel of size O(k6). Our results are based on a novel connection between Block Graph Vertex Deletion and the classical Feedback Vertex Set problem in graphs without induced C4 and K4 − e. To achieve our results we also obtain an algorithm for Weighted Feedback Vertex Set running in time 3.618knO(1) and improving over the running time of previously known algorithm with running time 5knO(1).

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SN - 9783662495285

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

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Agrawal A, Kolay S, Lokshtanov D, Saurabh S. A faster FPT algorithm and a smaller kernel for block graph vertex deletion. In Navarro G, Kranakis E, Chávez E, editors, LATIN 2016: Theoretical Informatics - 12th Latin American Symposium, Proceedings. Springer Verlag. 2016. p. 1-13. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). doi: 10.1007/978-3-662-49529-2_1

A faster FPT algorithm and a smaller kernel for block graph vertex deletion

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