Applications designed for data-parallel computation frameworks such as MapReduce usually alternate between computation and communication stages. Coflow scheduling is a recent popular networking abstraction introduced to capture such application-level communication patterns in datacenters. In this framework, a datacenter is modeled as a single non-blocking switch with m input ports and m output ports. A coflow j is a collection of flow demands {dioj}i∈{1,…,m},o∈{1,…,m}\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\{d^j_{io}\}_{i \in \{1,\ldots ,m\}, o \in \{1,\ldots ,m\}}$$\end{document} that is said to be complete once all of its requisite flows have been scheduled. We consider the offline coflow scheduling problem with and without release times to minimize the total weighted completion time. Coflow scheduling generalizes the well studied concurrent open shop scheduling problem and is thus NP-hard. Qiu et al. (in: ACM Symposium on parallelism in algorithms and architectures. ACM, New York, pp 294–303, 2015) obtain the first constant approximation algorithms for this problem via LP rounding and give a deterministic 673\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\frac{67}{3}$$\end{document}-approximation and a randomized (9+1623)≈16.54\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$(9 + \frac{16\sqrt{2}}{3}) \approx 16.54$$\end{document}-approximation algorithm. In this paper, we give a combinatorial algorithm that yields a deterministic 5-approximation algorithm for coflow scheduling with release times, and a deterministic 4-approximation for the case without release times. As for concurrent open shop problem with release times, we give a combinatorial 3-approximation algorithm.

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关于调度 Coflows

为数据并行计算框架（如 MapReduce）设计的应用程序通常在计算和通信阶段之间交替。Coflow 调度是最近引入的一种流行的网络抽象，用于捕获数据中心中的此类应用程序级通信模式。在此框架中，数据中心被建模为具有 m 个输入端口和 m 个输出端口的单个非阻塞交换机。coflow j 是流需求的集合 {dioj}i∈{1,…,m},o∈{1,…,m}\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \ usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\{d^j_{io}\ }_{i \in \{1,\ldots ,m\}, o \in \{1,\ldots ,m\}}$$\end{document} 据说一旦所有必需的流程就完成了已被安排。我们考虑有和没有释放时间的离线coflow调度问题，以最小化总加权完成时间。Coflow 调度概括了深入研究的并发开放式车间调度问题，因此是 NP-hard 问题。邱等人。(in: ACM Symposium on parallelism in algorithm and architectures. ACM, New York, pp 294–303, 2015) 通过 LP 舍入获得该问题的第一个常数近似算法，并给出确定性 673\documentclass[12pt]{minimal}\ usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$ $\frac{67}{3}$$\end{document}-近似和随机 (9+1623)≈16。54\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin} {-69pt} \begin{document}$$(9 + \frac{16\sqrt{2}}{3}) \approx 16.54$$\end{document}-近似算法。在本文中，我们给出了一种组合算法，该算法为具有释放时间的 coflow 调度产生确定性 5-近似算法，以及在没有释放时间的情况下产生确定性 4-近似算法。对于有发布时间的并发开店问题，我们给出了组合3-近似算法。在本文中，我们给出了一种组合算法，该算法为具有释放时间的 coflow 调度生成确定性 5-近似算法，并为没有释放时间的情况生成确定性 4-近似算法。对于有发布时间的并发开店问题，我们给出了组合3-近似算法。在本文中，我们给出了一种组合算法，该算法为具有释放时间的 coflow 调度产生确定性 5-近似算法，以及在没有释放时间的情况下产生确定性 4-近似算法。对于有发布时间的并发开店问题，我们给出了组合3-近似算法。