Interval vertex deletion admits a polynomial kernel

Akanksha Agrawal; Pranabendu Misra; Saket Saurabh; Meirav Zehavi

doi:10.1137/1.9781611975482.103

Interval vertex deletion admits a polynomial kernel

Akanksha Agrawal, Pranabendu Misra, Saket Saurabh, Meirav Zehavi

Department of Computer Science

Research output: Contribution to conference › Paper › peer-review

18 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 [Yannakakis, STOC’78]. Originally in 2012, Cao and Marx showed that IVD is fixed parameter tractable: they exhibited an algorithm with running time 10^kn^O⁽¹⁾ [Cao and Marx, SODA’14]. The existence of a polynomial kernel for IVD remained a well-known open problem in Parameterized Complexity. In this paper, we settle this problem in the affirmative. We also introduce a “bounded intersection” variant of the classical Two Families theorem of Bollobás. We believe this result will find further applications in combinatorics and algorithm design.

Original language	English
Pages	1711-1730
Number of pages	20
DOIs	https://doi.org/10.1137/1.9781611975482.103
State	Published - 1 Jan 2019
Event	30th Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2019 - San Diego, United States Duration: 6 Jan 2019 → 9 Jan 2019

Conference

Conference	30th Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2019
Country/Territory	United States
City	San Diego
Period	6/01/19 → 9/01/19

ASJC Scopus subject areas

Software
General Mathematics

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10.1137/1.9781611975482.103

Cite this

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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 [Yannakakis, STOC{\textquoteright}78]. Originally in 2012, Cao and Marx showed that IVD is fixed parameter tractable: they exhibited an algorithm with running time 10knO(1) [Cao and Marx, SODA{\textquoteright}14]. The existence of a polynomial kernel for IVD remained a well-known open problem in Parameterized Complexity. In this paper, we settle this problem in the affirmative. We also introduce a “bounded intersection” variant of the classical Two Families theorem of Bollob{\'a}s. We believe this result will find further applications in combinatorics and algorithm design.",

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AU - Misra, Pranabendu

AU - Saurabh, Saket

AU - Zehavi, Meirav

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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 [Yannakakis, STOC’78]. Originally in 2012, Cao and Marx showed that IVD is fixed parameter tractable: they exhibited an algorithm with running time 10knO(1) [Cao and Marx, SODA’14]. The existence of a polynomial kernel for IVD remained a well-known open problem in Parameterized Complexity. In this paper, we settle this problem in the affirmative. We also introduce a “bounded intersection” variant of the classical Two Families theorem of Bollobás. We believe this result will find further applications in combinatorics and algorithm design.

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T2 - 30th Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2019

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Interval vertex deletion admits a polynomial kernel

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