Tight Analysis of Relaxed Multi-organization Scheduling Algorithms

Daniel Cordeiro, P. Dutot, G. Mounié, D. Trystram
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引用次数: 10

Abstract

The goal of this paper is to study how limited cooperation can impact the quality of the schedule obtained by multiple independent organizations in a typical grid computing platform. This relaxed version of the problem known as the Multi-Organization Scheduling Problem (MOSP) models an environment where organizations providing both resources and jobs tolerate a bounded degradation on the make span of their own jobs in order to minimize the make span over the entire platform. More precisely, the technical contributions are the following. First, we improve the existing in approximation bounds for this problem proving that what was previously though as not polynomially approximable ({\it unless $P=NP$}) is actually not approximable at all. We achieve this using two families of instances whose Pareto optimal solutions are on par with the previous in aproximability bounds. Then, we present two algorithms that solve the problem with approximation ratios of (2, 3/2) and (3, 4/3) respectively. This means that when using the first (second) algorithm, if an organization tolerates that the completion time of its last job cannot exceed twice (three times) the time it would have obtained by itself, then the algorithm provides a solution that is a 3/2-approximation (4/3-approximation) for the optimal global make span. Both algorithms are efficient since their performance ratio correspond to the Pareto optimal solutions of the previously defined instances.
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松弛多组织调度算法的严密分析
本文的目的是研究在典型的网格计算平台中,有限的合作如何影响多个独立组织获得的调度质量。这个问题的宽松版本被称为多组织调度问题(MOSP),它对这样一种环境进行了建模,在这种环境中,提供资源和作业的组织为了最小化整个平台上的生产跨度,可以容忍他们自己的作业的生产跨度有限度的退化。更准确地说,技术贡献如下。首先,我们改进了这个问题的现有近似界,证明了以前虽然不是多项式近似的({\it除非$P=NP$})实际上根本不是近似的。我们使用两个实例族来实现这一目标,这两个实例族的Pareto最优解在近似界上与前面的Pareto最优解相同。然后,我们提出了两种算法,分别求解近似比为(2,3 /2)和(3,4 /3)的问题。这意味着,当使用第一(第二)算法时,如果一个组织允许其最后一个作业的完成时间不能超过它自己获得的时间的两倍(三倍),那么该算法提供的解决方案是最优全局make span的3/2近似(4/3近似)。这两种算法都是有效的,因为它们的性能比对应于前面定义的实例的帕累托最优解。
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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