树宽度的单指数时间2逼近算法

IF 1.2 3区计算机科学 Q3 COMPUTER SCIENCE, THEORY & METHODS

SIAM Journal on Computing Pub Date : 2023-11-14 DOI:10.1137/22m147551x

Tuukka Korhonen

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引用次数: 2

摘要

我们给出了一个算法，给定一个无顶点图和一个整数，在时间上要么输出一个最宽的树分解，要么确定树的宽度大于。这是第一个比已知精确算法更快的树宽2逼近算法，特别是在Bodlaender等人给出的5的最佳逼近比的基础上得到了改进。， 45 (2016)， pp. 317-378]。我们的算法通过将增量改进操作应用于树分解，使用一种受Bellenbaum和Diestel [Combin]证明启发的方法。Probab。第一版。， 11(2002)，第541-547页。

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A Single-Exponential Time 2-Approximation Algorithm for Treewidth

We give an algorithm that, given an -vertex graph and an integer , in time either outputs a tree decomposition of of width at most or determines that the treewidth of is larger than . This is the first 2-approximation algorithm for treewidth that is faster than the known exact algorithms, and in particular improves upon the previous best approximation ratio of 5 in time given by Bodlaender et al. [SIAM J. Comput., 45 (2016), pp. 317–378]. Our algorithm works by applying incremental improvement operations to a tree decomposition, using an approach inspired by a proof of Bellenbaum and Diestel [Combin. Probab. Comput., 11 (2002), pp. 541–547].

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来源期刊

SIAM Journal on Computing 工程技术-计算机：理论方法

CiteScore

4.60

自引率

0.00%

发文量

审稿时长

6-12 weeks

期刊介绍： The SIAM Journal on Computing aims to provide coverage of the most significant work going on in the mathematical and formal aspects of computer science and nonnumerical computing. Submissions must be clearly written and make a significant technical contribution. Topics include but are not limited to analysis and design of algorithms, algorithmic game theory, data structures, computational complexity, computational algebra, computational aspects of combinatorics and graph theory, computational biology, computational geometry, computational robotics, the mathematical aspects of programming languages, artificial intelligence, computational learning, databases, information retrieval, cryptography, networks, distributed computing, parallel algorithms, and computer architecture.