The parameterized complexity of cycle packing: Indifference is not an issue

R. Krithika; Abhishek Sahu; Saket Saurabh; Meirav Zehavi

doi:10.1007/978-3-319-77404-6_52

The parameterized complexity of cycle packing: Indifference is not an issue

R. Krithika, Abhishek Sahu, Saket Saurabh, Meirav Zehavi

Department of Computer Science

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

Abstract

In the Cycle Packing problem, we are given an undirected graph G, a positive integer r, and the task is to check whether there exist r vertex-disjoint cycles. In this paper, we study Cycle Packing with respect to a structural parameter, namely, distance to proper interval graphs (indifference graphs). In particular, we show that Cycle Packing is fixed-parameter tractable (FPT) when parameterized by t, the size of a proper interval deletion set. For this purpose, we design an algorithm with O(2 ^{O(t log t)}n^O(1)) running time. Several structural parameterizations for Cycle Packing have been studied in the literature and our FPT algorithm fills a gap in the ecology of such parameterizations. We combine color coding, greedy strategy and dynamic programming based on structural properties of proper interval graphs in a non-trivial fashion to obtain the FPT algorithm.

Original language	English
Title of host publication	LATIN 2018
Subtitle of host publication	Theoretical Informatics - 13th Latin American Symposium, Proceedings
Editors	Miguel A. Mosteiro, Michael A. Bender, Martin Farach-Colton
Publisher	Springer Verlag
Pages	712-726
Number of pages	15
ISBN (Print)	9783319774039
DOIs	https://doi.org/10.1007/978-3-319-77404-6_52
State	Published - 1 Jan 2018
Event	13th International Symposium on Latin American Theoretical Informatics, LATIN 2018 - Buenos Aires, Argentina Duration: 16 Apr 2018 → 19 Apr 2018

Publication series

Name	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume	10807 LNCS
ISSN (Print)	0302-9743
ISSN (Electronic)	1611-3349

Conference

Conference	13th International Symposium on Latin American Theoretical Informatics, LATIN 2018
Country/Territory	Argentina
City	Buenos Aires
Period	16/04/18 → 19/04/18

ASJC Scopus subject areas

Theoretical Computer Science
General Computer Science

Access to Document

10.1007/978-3-319-77404-6_52

Cite this

Krithika, R., Sahu, A., Saurabh, S., & Zehavi, M. (2018). The parameterized complexity of cycle packing: Indifference is not an issue. In M. A. Mosteiro, M. A. Bender, & M. Farach-Colton (Eds.), LATIN 2018: Theoretical Informatics - 13th Latin American Symposium, Proceedings (pp. 712-726). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 10807 LNCS). Springer Verlag. https://doi.org/10.1007/978-3-319-77404-6_52

Krithika, R. ; Sahu, Abhishek ; Saurabh, Saket et al. / The parameterized complexity of cycle packing : Indifference is not an issue. LATIN 2018: Theoretical Informatics - 13th Latin American Symposium, Proceedings. editor / Miguel A. Mosteiro ; Michael A. Bender ; Martin Farach-Colton. Springer Verlag, 2018. pp. 712-726 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).

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title = "The parameterized complexity of cycle packing: Indifference is not an issue",

abstract = "In the Cycle Packing problem, we are given an undirected graph G, a positive integer r, and the task is to check whether there exist r vertex-disjoint cycles. In this paper, we study Cycle Packing with respect to a structural parameter, namely, distance to proper interval graphs (indifference graphs). In particular, we show that Cycle Packing is fixed-parameter tractable (FPT) when parameterized by t, the size of a proper interval deletion set. For this purpose, we design an algorithm with O(2 O(t log t)nO(1)) running time. Several structural parameterizations for Cycle Packing have been studied in the literature and our FPT algorithm fills a gap in the ecology of such parameterizations. We combine color coding, greedy strategy and dynamic programming based on structural properties of proper interval graphs in a non-trivial fashion to obtain the FPT algorithm.",

author = "R. Krithika and Abhishek Sahu and Saket Saurabh and Meirav Zehavi",

note = "Publisher Copyright: {\textcopyright} Springer International Publishing AG, part of Springer Nature 2018.; 13th International Symposium on Latin American Theoretical Informatics, LATIN 2018 ; Conference date: 16-04-2018 Through 19-04-2018",

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doi = "10.1007/978-3-319-77404-6_52",

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Krithika, R, Sahu, A, Saurabh, S & Zehavi, M 2018, The parameterized complexity of cycle packing: Indifference is not an issue. in MA Mosteiro, MA Bender & M Farach-Colton (eds), LATIN 2018: Theoretical Informatics - 13th Latin American Symposium, Proceedings. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 10807 LNCS, Springer Verlag, pp. 712-726, 13th International Symposium on Latin American Theoretical Informatics, LATIN 2018, Buenos Aires, Argentina, 16/04/18. https://doi.org/10.1007/978-3-319-77404-6_52

The parameterized complexity of cycle packing: Indifference is not an issue. / Krithika, R.; Sahu, Abhishek; Saurabh, Saket et al.
LATIN 2018: Theoretical Informatics - 13th Latin American Symposium, Proceedings. ed. / Miguel A. Mosteiro; Michael A. Bender; Martin Farach-Colton. Springer Verlag, 2018. p. 712-726 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 10807 LNCS).

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

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T1 - The parameterized complexity of cycle packing

T2 - 13th International Symposium on Latin American Theoretical Informatics, LATIN 2018

AU - Krithika, R.

AU - Sahu, Abhishek

AU - Saurabh, Saket

AU - Zehavi, Meirav

PY - 2018/1/1

Y1 - 2018/1/1

N2 - In the Cycle Packing problem, we are given an undirected graph G, a positive integer r, and the task is to check whether there exist r vertex-disjoint cycles. In this paper, we study Cycle Packing with respect to a structural parameter, namely, distance to proper interval graphs (indifference graphs). In particular, we show that Cycle Packing is fixed-parameter tractable (FPT) when parameterized by t, the size of a proper interval deletion set. For this purpose, we design an algorithm with O(2 O(t log t)nO(1)) running time. Several structural parameterizations for Cycle Packing have been studied in the literature and our FPT algorithm fills a gap in the ecology of such parameterizations. We combine color coding, greedy strategy and dynamic programming based on structural properties of proper interval graphs in a non-trivial fashion to obtain the FPT algorithm.

AB - In the Cycle Packing problem, we are given an undirected graph G, a positive integer r, and the task is to check whether there exist r vertex-disjoint cycles. In this paper, we study Cycle Packing with respect to a structural parameter, namely, distance to proper interval graphs (indifference graphs). In particular, we show that Cycle Packing is fixed-parameter tractable (FPT) when parameterized by t, the size of a proper interval deletion set. For this purpose, we design an algorithm with O(2 O(t log t)nO(1)) running time. Several structural parameterizations for Cycle Packing have been studied in the literature and our FPT algorithm fills a gap in the ecology of such parameterizations. We combine color coding, greedy strategy and dynamic programming based on structural properties of proper interval graphs in a non-trivial fashion to obtain the FPT algorithm.

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SN - 9783319774039

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

SP - 712

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PB - Springer Verlag

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ER -

Krithika R, Sahu A, Saurabh S, Zehavi M. The parameterized complexity of cycle packing: Indifference is not an issue. In Mosteiro MA, Bender MA, Farach-Colton M, editors, LATIN 2018: Theoretical Informatics - 13th Latin American Symposium, Proceedings. Springer Verlag. 2018. p. 712-726. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). doi: 10.1007/978-3-319-77404-6_52

The parameterized complexity of cycle packing: Indifference is not an issue

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