Akanksha Agrawal, Daniel Lokshtanov, Pranabendu Misra, Saket Saurabh, Meirav Zehavi
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引用次数: 0
摘要
给定一个图G和一个整数k，区间顶点删除(IVD)问题问是否存在一个最大为k的子集S≠V(G)，使得G−S是一个区间图。已知这个问题是np完全的[Yannakakis, STOC ' 78]。最初在2012年，Cao和Marx证明了IVD是固定参数可处理的:他们展示了一个具有运行时间\(10^k n^{\mathcal {O}(1)} \)的算法[Cao和Marx, SODA ' 14]。IVD的多项式核是否存在是参数化复杂度中一个众所周知的开放性问题。本文对这一问题作了肯定的解决。
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 \(10^k n^{\mathcal {O}(1)} \) [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.
期刊介绍：
ACM Transactions on Algorithms welcomes submissions of original research of the highest quality dealing with algorithms that are inherently discrete and finite, and having mathematical content in a natural way, either in the objective or in the analysis. Most welcome are new algorithms and data structures, new and improved analyses, and complexity results. Specific areas of computation covered by the journal include
combinatorial searches and objects;
counting;
discrete optimization and approximation;
randomization and quantum computation;
parallel and distributed computation;
algorithms for
graphs,
geometry,
arithmetic,
number theory,
strings;
on-line analysis;
cryptography;
coding;
data compression;
learning algorithms;
methods of algorithmic analysis;
discrete algorithms for application areas such as
biology,
economics,
game theory,
communication,
computer systems and architecture,
hardware design,
scientific computing
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