Polynomial Kernel for Interval Vertex Deletion

IF 0.9 3区计算机科学 Q3 COMPUTER SCIENCE, THEORY & METHODS

ACM Transactions on Algorithms Pub Date : 2023-01-19 DOI:10.1145/3571075

A. Agrawal, D. Lokshtanov, P. Misra, Saket Saurabh, M. Zehavi

引用次数: 0

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.

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区间顶点删除的多项式核

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。这个问题已知是np完全的(根据Yannakakis在STOC 1978)。最早在2012年，Cao和Marx证明了IVD是固定参数可处理的:他们展示了一个运行时间为10k nO(1)的算法。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论述。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

ACM Transactions on Algorithms COMPUTER SCIENCE, THEORY & METHODS-MATHEMATICS, APPLIED

CiteScore

3.30

自引率

0.00%

发文量

审稿时长

6-12 weeks

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