Polynomial Kernel for Interval Vertex Deletion-Reference-Cited by-同舟云学术

Polynomial Kernel for Interval Vertex Deletion

Published:2023-04-15 Issue:2 Volume:19 Page:1-68
ISSN:1549-6325
Container-title:ACM Transactions on Algorithms
language:en
Short-container-title:ACM Trans. Algorithms

Author:

Agrawal Akanksha¹^ORCID,Lokshtanov Daniel²^ORCID,Misra Pranabendu³^ORCID,Saurabh Saket⁴^ORCID,Zehavi Meirav⁵^ORCID

Affiliation:

1. Indian Institute of Technology Madras, Chennai, India

2. University of California, Santa Barbara, Santa Barbara, CA

3. Chennai Mathematical Institute, Chennai, India

4. Homi Bhabha National Institute, Chennai, India, and University of Bergen, Bergen, Norway

5. Ben-Gurion University, Beersheba, Israel

Abstract

Given a graph G and an integer k , the Interval Vertex Deletion (IVD) problem asks whether there exists a subset S ⊆ V ( G ) of size at most k such that G-S is an interval graph. This problem is known to be NP -complete (according to Yannakakis at STOC 1978). Originally in 2012, Cao and Marx showed that IVD is fixed parameter tractable: they exhibited an algorithm with running time 10 k n O (1). The existence of a polynomial kernel for IVD remained a well-known open problem in parameterized complexity. In this article, we settle this problem in the affirmative.

Funder

European Research Council

PaPaAlg

SYSTEM-ATICGRAPH

Israel Science Foundation

New Faculty Initiation

Science and Engineering Research Board

NSF

European Union’s Horizon 2020

Swarnajayanti Fellowship

Publisher

Association for Computing Machinery (ACM)

Subject

Mathematics (miscellaneous)

Link

https://dl.acm.org/doi/pdf/10.1145/3571075

Reference53 articles.

1. Akanksha Agrawal Sudeshna Kolay Daniel Lokshtanov and Saket Saurabh. 2016. A faster FPT algorithm and a smaller kernel for block graph vertex deletion. In LATIN 2016: Theoretical Informatics . Lecture Notes in Computer Science Vol. 9644. Springer 1–13.

2. Akanksha Agrawal, Daniel Lokshtanov, Pranabendu Misra, Saket Saurabh, and Meirav Zehavi. 2017. Feedback vertex set inspired kernel for chordal vertex deletion. In Proceedings of the 28th Annual ACM-SIAM Symposium on Discrete Algorithms (SODA’17). SIAM, 1383–1398.

3. Feedback vertex set inspired kernel for chordal vertex deletion;Agrawal Akanksha;ACM Transactions on Algorithms,2019

4. Simultaneous feedback vertex set: A parameterized perspective;Agrawal Akanksha;ACM Transactions on Computation Theory,2018

5. A unified approach to approximating resource allocation and scheduling