Polynomial Kernel for Interval Vertex Deletion

Akanksha Agrawal; Daniel Lokshtanov; Pranabendu Misra; Saket Saurabh; Meirav Zehavi

doi:10.1145/3571075

Polynomial Kernel for Interval Vertex Deletion

Akanksha Agrawal
, Daniel Lokshtanov
, Pranabendu Misra
, Saket Saurabh
, Meirav Zehavi

Research output: Contribution to journal › Article › peer-review

2 Scopus citations

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 10k nO(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.

Original language	English
Article number	11
Journal	ACM Transactions on Algorithms
Volume	19
Issue number	2
DOIs	https://doi.org/10.1145/3571075
State	Published - 15 Apr 2023

Keywords

Interval Vertex Deletion
kernelization
parameterized complexity
polynomial kernel

ASJC Scopus subject areas

Mathematics (miscellaneous)

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10.1145/3571075

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title = "Polynomial Kernel for Interval Vertex Deletion",

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 10k nO(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.",

keywords = "Interval Vertex Deletion, kernelization, parameterized complexity, polynomial kernel",

author = "Akanksha Agrawal and Daniel Lokshtanov and Pranabendu Misra and Saket Saurabh and Meirav Zehavi",

note = "Publisher Copyright: {\textcopyright} 2023 Copyright held by the owner/author(s). Publication rights licensed to ACM.",

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T1 - Polynomial Kernel for Interval Vertex Deletion

AU - Agrawal, Akanksha

AU - Lokshtanov, Daniel

AU - Misra, Pranabendu

AU - Saurabh, Saket

AU - Zehavi, Meirav

PY - 2023/4/15

Y1 - 2023/4/15

N2 - 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 10k nO(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.

AB - 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 10k nO(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.

KW - Interval Vertex Deletion

KW - kernelization

KW - parameterized complexity

KW - polynomial kernel

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SN - 1549-6325

VL - 19

JO - ACM Transactions on Algorithms

JF - ACM Transactions on Algorithms

IS - 2

M1 - 11

ER -

Polynomial Kernel for Interval Vertex Deletion

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Keywords

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