当前位置: X-MOL 学术J. Sched. › 论文详情
Our official English website, www.x-mol.net, welcomes your feedback! (Note: you will need to create a separate account there.)
Broadcasting a file in a communication network
Journal of Scheduling ( IF 2 ) Pub Date : 2020-02-11 , DOI: 10.1007/s10951-020-00643-w
Kai-Simon Goetzmann , Tobias Harks , Max Klimm

We study the problem of distributing a file, initially located at a server, among a set of n nodes. The file is divided into $$m\ge 1$$ m ≥ 1 equally sized packets. After downloading a packet, nodes can upload it to other nodes, possibly to multiple nodes in parallel. Each node, however, may receive each packet from a single source node only. The upload and download rates between nodes are constrained by node- and server-specific upload and download capacities. The objective is to minimize the makespan. This problem has been proposed and analyzed first by Mundinger et al. (J Sched 11:105–120, 2008 . https://doi.org/10.1007/s10951-007-0017-9 ) under the assumption that uploads obey the fair sharing principle, that is, concurrent upload rates from a common source are equal at any point in time. Under this assumption, the authors devised an optimal polynomial time algorithm for the case where the upload capacity of the server and the nodes’ upload and download capacities are all equal. In this work, we drop the fair sharing assumption and derive an exact polynomial time algorithm for the case when upload and download capacities per node and among nodes are equal. We further show that the problem becomes strongly NP-hard for equal upload and download capacities per node that may differ among nodes, even for a single packet. For this case, we devise a polynomial time $$\smash {(1+2\sqrt{2})}$$ ( 1 + 2 2 ) -approximation algorithm. Finally, we devise two polynomial time algorithms with approximation guarantees of 5 and $$2 + \lceil \log _2 \lceil n/m\rceil \rceil /m$$ 2 + ⌈ log 2 ⌈ n / m ⌉ ⌉ / m , respectively, for the general case of m packets.

中文翻译:

在通信网络中广播文件

我们研究在一组 n 个节点之间分发最初位于服务器上的文件的问题。该文件被分成 $$m\ge 1$$ m ≥ 1 个大小相同的数据包。下载数据包后,节点可以将其上传到其他节点,也可以并行上传到多个节点。然而,每个节点只能从单个源节点接收每个数据包。节点之间的上传和下载速率受节点和服务器特定上传和下载容量的限制。目标是最小化完工时间。Mundinger 等人首先提出并分析了这个问题。(J Sched 11:105–120, 2008 . https://doi.org/10.1007/s10951-007-0017-9 )假设上传遵循公平共享原则,即来自共同来源的并发上传率在任何时间点都是相等的。在这个假设下,针对服务器的上传能力和节点的上传下载能力都相等的情况,作者设计了一种最优多项式时间算法。在这项工作中,我们放弃了公平共享假设,并针对每个节点和节点之间的上传和下载容量相等的情况推导出精确的多项式时间算法。我们进一步表明,对于每个节点相同的上传和下载容量,即使对于单个数据包,在节点之间也可能不同,问题变得非常 NP-hard。对于这种情况,我们设计了一个多项式时间 $$\smash {(1+2\sqrt{2})}$$ ( 1 + 2 2 ) - 近似算法。最后,我们设计了两个近似保证为 5 和 $$2 + \lceil \log _2 \lceil n/m\rceil \rceil /m$$ 2 + ⌈ log 2 ⌈ n / m ⌉ ⌉ / m 的多项式时间算法,对于 m 个数据包的一般情况。
更新日期:2020-02-11
down
wechat
bug