最小k边连通生成子图的分布逼近

Michal Dory
{"title":"最小k边连通生成子图的分布逼近","authors":"Michal Dory","doi":"10.1145/3212734.3212760","DOIUrl":null,"url":null,"abstract":"In the minimum k-edge-connected spanning subgraph (k-ECSS) problem the goal is to find the minimum weight subgraph resistant to up to k-1 edge failures. This is a central problem in network design, and a natural generalization of the minimum spanning tree (MST) problem. While the MST problem has been studied extensively by the distributed computing community, for k ≥2 less is known in the distributed setting. In this paper, we present fast randomized distributed approximation algorithms for k-ECSS in the CONGEST model. Our first contribution is an Õ (D + √ )-round O(logn )-approximation for 2-ECSS, for a graph with n vertices and diameter D. The time complexity of our algorithm is almost tight and almost matches the time complexity of the MST problem. For larger constant values of k we give an Õ (n) -round O(logn ) -approximation. Additionally, in the special case of unweighted 3-ECSS we show how to improve the time complexity to O(D log^3n ) rounds. All our results significantly improve the time complexity of previous algorithms.","PeriodicalId":198284,"journal":{"name":"Proceedings of the 2018 ACM Symposium on Principles of Distributed Computing","volume":null,"pages":null},"PeriodicalIF":0.0000,"publicationDate":"2018-05-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"14","resultStr":"{\"title\":\"Distributed Approximation of Minimum k-edge-connected Spanning Subgraphs\",\"authors\":\"Michal Dory\",\"doi\":\"10.1145/3212734.3212760\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"In the minimum k-edge-connected spanning subgraph (k-ECSS) problem the goal is to find the minimum weight subgraph resistant to up to k-1 edge failures. This is a central problem in network design, and a natural generalization of the minimum spanning tree (MST) problem. While the MST problem has been studied extensively by the distributed computing community, for k ≥2 less is known in the distributed setting. In this paper, we present fast randomized distributed approximation algorithms for k-ECSS in the CONGEST model. Our first contribution is an Õ (D + √ )-round O(logn )-approximation for 2-ECSS, for a graph with n vertices and diameter D. The time complexity of our algorithm is almost tight and almost matches the time complexity of the MST problem. For larger constant values of k we give an Õ (n) -round O(logn ) -approximation. Additionally, in the special case of unweighted 3-ECSS we show how to improve the time complexity to O(D log^3n ) rounds. All our results significantly improve the time complexity of previous algorithms.\",\"PeriodicalId\":198284,\"journal\":{\"name\":\"Proceedings of the 2018 ACM Symposium on Principles of Distributed Computing\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2018-05-20\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"14\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Proceedings of the 2018 ACM Symposium on Principles of Distributed Computing\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1145/3212734.3212760\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Proceedings of the 2018 ACM Symposium on Principles of Distributed Computing","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1145/3212734.3212760","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 14

摘要

在最小k边连通生成子图(k-ECSS)问题中,目标是找到能抵抗最多k-1个边失效的最小权值子图。这是网络设计中的一个核心问题,也是最小生成树(MST)问题的自然推广。尽管分布式计算社区已经对MST问题进行了广泛的研究,但对于k≥2,在分布式设置中已知的较少。本文给出了CONGEST模型中k-ECSS的快速随机分布近似算法。我们的第一个贡献是对于2-ECSS的Õ (D +√)-round O(logn)-近似,对于n个顶点和直径D的图,我们的算法的时间复杂度几乎很紧,几乎与MST问题的时间复杂度相匹配。对于较大的常数k,我们给出Õ (n) - O(logn) -近似。此外,在非加权3-ECSS的特殊情况下,我们展示了如何将时间复杂度提高到O(D log^3n)轮。我们的结果都显著提高了以前算法的时间复杂度。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
查看原文
分享 分享
微信好友 朋友圈 QQ好友 复制链接
本刊更多论文
Distributed Approximation of Minimum k-edge-connected Spanning Subgraphs
In the minimum k-edge-connected spanning subgraph (k-ECSS) problem the goal is to find the minimum weight subgraph resistant to up to k-1 edge failures. This is a central problem in network design, and a natural generalization of the minimum spanning tree (MST) problem. While the MST problem has been studied extensively by the distributed computing community, for k ≥2 less is known in the distributed setting. In this paper, we present fast randomized distributed approximation algorithms for k-ECSS in the CONGEST model. Our first contribution is an Õ (D + √ )-round O(logn )-approximation for 2-ECSS, for a graph with n vertices and diameter D. The time complexity of our algorithm is almost tight and almost matches the time complexity of the MST problem. For larger constant values of k we give an Õ (n) -round O(logn ) -approximation. Additionally, in the special case of unweighted 3-ECSS we show how to improve the time complexity to O(D log^3n ) rounds. All our results significantly improve the time complexity of previous algorithms.
求助全文
通过发布文献求助,成功后即可免费获取论文全文。 去求助
来源期刊
自引率
0.00%
发文量
0
期刊最新文献
Tutorial: Consistency Choices in Modern Distributed Systems Locking Timestamps versus Locking Objects Recoverable Mutual Exclusion Under System-Wide Failures Nesting-Safe Recoverable Linearizability: Modular Constructions for Non-Volatile Memory Brief Announcement: Beeping a Time-Optimal Leader Election
×
引用
GB/T 7714-2015
复制
MLA
复制
APA
复制
导出至
BibTeX EndNote RefMan NoteFirst NoteExpress
×
×
提示
您的信息不完整,为了账户安全,请先补充。
现在去补充
×
提示
您因"违规操作"
具体请查看互助需知
我知道了
×
提示
现在去查看 取消
×
提示
确定
0
微信
客服QQ
Book学术公众号 扫码关注我们
反馈
×
意见反馈
请填写您的意见或建议
请填写您的手机或邮箱
已复制链接
已复制链接
快去分享给好友吧!
我知道了
×
扫码分享
扫码分享
Book学术官方微信
Book学术文献互助
Book学术文献互助群
群 号:481959085
Book学术
文献互助 智能选刊 最新文献 互助须知 联系我们:info@booksci.cn
Book学术提供免费学术资源搜索服务,方便国内外学者检索中英文文献。致力于提供最便捷和优质的服务体验。
Copyright © 2023 Book学术 All rights reserved.
ghs 京公网安备 11010802042870号 京ICP备2023020795号-1