A PTAS for k-hop MST on the Euclidean plane: Improving dependency on k

IF 0.7 4区计算机科学 Q4 COMPUTER SCIENCE, INFORMATION SYSTEMS

Information Processing Letters Pub Date : 2025-04-15 DOI:10.1016/j.ipl.2025.106581

Jittat Fakcharoenphol , Nonthaphat Wongwattanakij

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引用次数: 0

Abstract

For any

ϵ > 0

, Laue and Matijević [CCCG'07, IPL'08] give a PTAS for finding a

(1 + ϵ)

-approximate solution to the k-hop MST problem in the Euclidean plane that runs in time

{(n / ϵ)}^{O (k / ϵ)}

. In this paper, we present an algorithm that runs in time

{(n / ϵ)}^{O (\log k \cdot {(1 / ϵ)}^{2} \cdot \log^{2} (1 / ϵ))}

. This gives an improvement on the dependency on k on the exponent, while having a worse dependency on ϵ. As in Laue and Matijević, we follow the framework introduced by Arora for Euclidean TSP. Our key ingredients include exponential distance scaling and compression of dynamic programming state tables.

查看原文本刊更多论文

欧几里得平面上k-hop MST的PTAS：改进对k的依赖

对于任何ϵ>；0， Laue和matijeviki [CCCG'07， IPL'08]给出了在欧几里得平面上寻找k-hop MST问题（1+ λ）近似解的PTAS，该问题运行时间为（n/ λ）O（k/ λ）。在本文中，我们提出了一种运行时间为（n/ λ）O(log （k·（1/ λ）2·log2 (1/ λ)）的算法。这改善了指数对k的依赖性，而对λ的依赖性更差。与Laue和matijeviki一样，我们遵循Arora为欧几里得TSP引入的框架。我们的关键成分包括指数距离缩放和压缩动态规划状态表。

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

Information Processing Letters 工程技术-计算机：信息系统

CiteScore

1.80

自引率

0.00%

发文量

审稿时长

7.3 months

期刊介绍： Information Processing Letters invites submission of original research articles that focus on fundamental aspects of information processing and computing. This naturally includes work in the broadly understood field of theoretical computer science; although papers in all areas of scientific inquiry will be given consideration, provided that they describe research contributions credibly motivated by applications to computing and involve rigorous methodology. High quality experimental papers that address topics of sufficiently broad interest may also be considered. Since its inception in 1971, Information Processing Letters has served as a forum for timely dissemination of short, concise and focused research contributions. Continuing with this tradition, and to expedite the reviewing process, manuscripts are generally limited in length to nine pages when they appear in print.