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

Department of Computer Science

Ben-Gurion University of the Negev

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

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	American 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

All Science Journal Classification (ASJC) codes

Mathematics (miscellaneous)

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10.1145/3571075

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AU - Lokshtanov, Daniel

AU - Misra, Pranabendu

AU - Saurabh, Saket

AU - Zehavi, Meirav

PY - 2023/4/15

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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.

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KW - kernelization

KW - parameterized complexity

KW - polynomial kernel

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JF - ACM Transactions on Algorithms

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ER -

Polynomial Kernel for Interval Vertex Deletion

Abstract

Keywords

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