度量空间中所有点最远对的逼近与最大生成树

IF 0.6 4区计算机科学 Q4 COMPUTER SCIENCE, THEORY & METHODS

International Journal of Foundations of Computer Science Pub Date : 2023-09-07 DOI:10.1142/s0129054123500181

Ching-Lueh Chang, Chun-Wei Chang

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引用次数: 0

摘要

考虑在度量空间[公式:见文本]中为每个点[公式:见文本]找到距离[公式:见文本]最远的点的问题，其中[公式:见文本]。我们证明了这个问题有一个确定性的[公式:见文]-时间[公式:见文]-近似算法。作为推论，度量空间中的最大生成树问题具有确定性的[公式:见文]-时间[公式:见文]-近似算法。我们还给出了一个蒙特卡罗[公式:见文]时间算法输出，对于每个[公式:见文]，一个点[公式:见文]满足[公式:见文]，其中[公式:见文]。作为推论，我们有一个蒙特卡罗[公式:见文本]时间算法，用于在[公式:见文本]中找到一个权重至少为[公式:见文本]的生成树。

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Approximating All-Points Furthest Pairs and Maximum Spanning Trees in Metric Spaces

Consider the problem of finding a point furthest from [Formula: see text] for each point [Formula: see text] in a metric space [Formula: see text], where [Formula: see text]. We prove this problem to have a deterministic [Formula: see text]-time [Formula: see text]-approximation algorithm. As a corollary, the maximum spanning tree problem in metric spaces has a deterministic [Formula: see text]-time [Formula: see text]-approximation algorithm. We also give a Monte Carlo [Formula: see text]-time algorithm outputting, for each [Formula: see text], a point [Formula: see text] satisfying [Formula: see text], where [Formula: see text]. As a corollary, we have a Monte Carlo [Formula: see text]-time algorithm for finding a spanning tree of weight at least [Formula: see text] in [Formula: see text].

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来源期刊

International Journal of Foundations of Computer Science 工程技术-计算机：理论方法

CiteScore

1.60

自引率

12.50%

发文量

审稿时长

3 months

期刊介绍： The International Journal of Foundations of Computer Science is a bimonthly journal that publishes articles which contribute new theoretical results in all areas of the foundations of computer science. The theoretical and mathematical aspects covered include: - Algebraic theory of computing and formal systems - Algorithm and system implementation issues - Approximation, probabilistic, and randomized algorithms - Automata and formal languages - Automated deduction - Combinatorics and graph theory - Complexity theory - Computational biology and bioinformatics - Cryptography - Database theory - Data structures - Design and analysis of algorithms - DNA computing - Foundations of computer security - Foundations of high-performance computing