@article{a3cc411c64764f7aa5e384eec2ce12ed,
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 = "Funding Information: The research leading to these results received funding from the European Research Council under ERC Starting Grant PARAPPROX (no. 306992), ERC Starting Grant PaPaAlg (no. 715744), ERC Consolidator Grant SYSTEM-ATICGRAPH (no. 725978), and an Israel Science Foundation (ISF) grant (no. 1176/18). Currently, A. Agrawal is supported by the New Faculty Initiation Grant (NFIG008972) and the Startup Research Grant from the Science and Engineering Research Board (SRG/2002/000962), D. Lokshtanov is supported by NSF award CCF2008838, S. Saurabh is supported by the European Research Council (ERC) under the European Union{\textquoteright}s Horizon 2020 research and innovation programme (no. 819416) and the Swarnajayanti Fellowship (no. DST/SJF/MSA01/2017-18), and M. Zehavi is supported by the European Research Council (ERC) grant titled PARAPATH. Funding Information: The research leading to these results received funding from the European Research Council under ERC Starting Grant PARAPPROX (no. 306992), ERC Starting Grant PaPaAlg (no. 715744), ERC Consolidator Grant SYSTEM-ATICGRAPH (no. 725978), and an Israel Science Foundation (ISF) grant (no. 1176/18). Currently, A. Agrawal is supported by the New Faculty Initiation Grant (NFIG008972) and the Startup Research Grant from the Science and Engineering Research Board (SRG/2002/000962), D. Lokshtanov is supported by NSF award CCF2008838, S. Saurabh is supported by the European Research Council (ERC) under the European Union's Horizon 2020 research and innovation programme (no. 819416) and the Swarnajayanti Fellowship (no. DST/SJF/MSA01/2017-18), and M. Zehavi is supported by the European Research Council (ERC) grant titled PARAPATH. Publisher Copyright: {\textcopyright} 2023 Copyright held by the owner/author(s). Publication rights licensed to ACM.",
year = "2023",
month = apr,
day = "15",
doi = "10.1145/3571075",
language = "English",
volume = "19",
journal = "ACM Transactions on Algorithms",
issn = "1549-6325",
publisher = "Association for Computing Machinery (ACM)",
number = "2",
}