research-article

Interval Deletion Is Fixed-Parameter Tractable

Authors:

Dániel MarxAuthors Info & Claims

ACM Transactions on Algorithms (TALG), Volume 11, Issue 3

Article No.: 21, Pages 1 - 35

https://doi.org/10.1145/2629595

Published: 13 January 2015 Publication History

Abstract

We study the minimum interval deletion problem, which asks for the removal of a set of at most k vertices to make a graph of n vertices into an interval graph. We present a parameterized algorithm of runtime 10^k ⋅ n^O(1) for this problem—that is, we show that the problem is fixed-parameter tractable.

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Cited By

Włodarczyk M(2025)Tight Bounds for Chordal/Interval Vertex Deletion Parameterized by TreewidthAlgorithmica10.1007/s00453-025-01293-0Online publication date: 29-Jan-2025
https://doi.org/10.1007/s00453-025-01293-0
Cao YYuan HWang J(2024)Modification problems toward proper (Helly) circular-arc graphsInformation and Computation10.1016/j.ic.2024.105211301(105211)Online publication date: Dec-2024
https://doi.org/10.1016/j.ic.2024.105211
Agrawal ALokshtanov DMisra PSaurabh SZehavi M(2023)Polynomial Kernel for Interval Vertex DeletionACM Transactions on Algorithms10.1145/357107519:2(1-68)Online publication date: 15-Apr-2023
https://dl.acm.org/doi/10.1145/3571075
Show More Cited By

Index Terms

Interval Deletion Is Fixed-Parameter Tractable
1. Mathematics of computing
  1. Discrete mathematics
    1. Graph theory
2. Theory of computation
  1. Design and analysis of algorithms

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cover image ACM Transactions on Algorithms

ACM Transactions on Algorithms Volume 11, Issue 3

January 2015

269 pages

ISSN:1549-6325

EISSN:1549-6333

DOI:10.1145/2721890

Editor:
Aravind Srinivasan
University of Maryland, USA

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Copyright © 2015 ACM.

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Association for Computing Machinery

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Publication History

Published: 13 January 2015

Accepted: 01 April 2014

Revised: 01 January 2014

Received: 01 May 2013

Published in TALG Volume 11, Issue 3

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Cited By

Włodarczyk M(2025)Tight Bounds for Chordal/Interval Vertex Deletion Parameterized by TreewidthAlgorithmica10.1007/s00453-025-01293-0Online publication date: 29-Jan-2025
https://doi.org/10.1007/s00453-025-01293-0
Cao YYuan HWang J(2024)Modification problems toward proper (Helly) circular-arc graphsInformation and Computation10.1016/j.ic.2024.105211301(105211)Online publication date: Dec-2024
https://doi.org/10.1016/j.ic.2024.105211
Agrawal ALokshtanov DMisra PSaurabh SZehavi M(2023)Polynomial Kernel for Interval Vertex DeletionACM Transactions on Algorithms10.1145/357107519:2(1-68)Online publication date: 15-Apr-2023
https://dl.acm.org/doi/10.1145/3571075
Agrawal ABhattacharjee SJana SSahu A(2023)Parameterized complexity of perfectly matched setsTheoretical Computer Science10.1016/j.tcs.2023.113861958:COnline publication date: 22-May-2023
https://dl.acm.org/doi/10.1016/j.tcs.2023.113861
Jacob Ade Kroon JMajumdar DRaman V(2023)Deletion to scattered graph classes I - Case of finite number of graph classesJournal of Computer and System Sciences10.1016/j.jcss.2023.05.005138(103460)Online publication date: Dec-2023
https://doi.org/10.1016/j.jcss.2023.05.005
Jacob AMajumdar DRaman V(2023)Deletion to scattered graph classes II - improved FPT algorithms for deletion to pairs of graph classesJournal of Computer and System Sciences10.1016/j.jcss.2023.03.004136(280-301)Online publication date: Sep-2023
https://doi.org/10.1016/j.jcss.2023.03.004
Crespelle CDrange PFomin FGolovach P(2023)A survey of parameterized algorithms and the complexity of edge modificationComputer Science Review10.1016/j.cosrev.2023.10055648(100556)Online publication date: May-2023
https://doi.org/10.1016/j.cosrev.2023.100556
Bishnu AGhosh AKolay SMishra GSaurabh S(2023)Small Vertex Cover Helps in Fixed-Parameter Tractability of Graph Deletion Problems over Data StreamsTheory of Computing Systems10.1007/s00224-023-10136-w67:6(1241-1267)Online publication date: 20-Sep-2023
https://doi.org/10.1007/s00224-023-10136-w
Ahn JKim ELee E(2022)Towards Constant-Factor Approximation for Chordal/Distance-Hereditary Vertex DeletionAlgorithmica10.1007/s00453-022-00963-784:7(2106-2133)Online publication date: 1-Jul-2022
https://dl.acm.org/doi/10.1007/s00453-022-00963-7
Agrawal ARamanujan M(2022)Distance from Triviality 2.0: Hybrid ParameterizationsCombinatorial Algorithms10.1007/978-3-031-06678-8_1(3-20)Online publication date: 7-Jun-2022
https://dl.acm.org/doi/10.1007/978-3-031-06678-8_1
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