Generalizing Horn's conditions for preemptive scheduling on identical parallel machines via network flow techniques

IF 1.6 4区计算机科学 Q4 COMPUTER SCIENCE, HARDWARE & ARCHITECTURE Networks Pub Date : 2023-12-20 DOI:10.1002/net.22202

Akiyoshi Shioura, Vitaly A. Strusevich, Natalia V. Shakhlevich

引用次数: 0

Abstract

We study the use of flow-based algorithmic and proof techniques applied to preemptive scheduling of jobs on parallel identical machines. For the classical problem in which the jobs have individual release dates and must be finished by a common deadline, we present and prove unified necessary and sufficient conditions for the existence of a feasible schedule by examining the structure of minimum cuts in a special network. We then study an enhanced model that allows the presence of additional resources, provided that some jobs at any time of their processing require one unit of a particular resource. We extend our argument developed for the classical case to this enhanced model. The generalized necessary and sufficient conditions for the existence of a feasible schedule are presented and proved using the max-flow/min-cut reasoning.

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通过网络流技术推广相同并行机上抢占式调度的霍恩条件

我们研究了基于流的算法和证明技术在并行相同机器上作业抢先调度中的应用。对于作业有各自的发布日期且必须在共同截止日期前完成的经典问题，我们通过研究特殊网络中最小切割的结构，提出并证明了可行调度存在的统一必要条件和充分条件。然后，我们研究了一个允许额外资源存在的增强模型，条件是某些作业在其处理过程中的任何时候都需要一个单位的特定资源。我们将针对经典模型的论证扩展到这一增强模型。我们提出了可行计划表存在的广义必要条件和充分条件，并使用最大流量/最小切分推理进行了证明。

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

Networks 工程技术-计算机：硬件

CiteScore

4.40

自引率

9.50%

发文量

审稿时长

12 months

期刊介绍： Network problems are pervasive in our modern technological society, as witnessed by our reliance on physical networks that provide power, communication, and transportation. As well, a number of processes can be modeled using logical networks, as in the scheduling of interdependent tasks, the dating of archaeological artifacts, or the compilation of subroutines comprising a large computer program. Networks provide a common framework for posing and studying problems that often have wider applicability than their originating context. The goal of this journal is to provide a central forum for the distribution of timely information about network problems, their design and mathematical analysis, as well as efficient algorithms for carrying out optimization on networks. The nonstandard modeling of diverse processes using networks and network concepts is also of interest. Consequently, the disciplines that are useful in studying networks are varied, including applied mathematics, operations research, computer science, discrete mathematics, and economics. Networks publishes material on the analytic modeling of problems using networks, the mathematical analysis of network problems, the design of computationally eﬃcient network algorithms, and innovative case studies of successful network applications. We do not typically publish works that fall in the realm of pure graph theory (without signiﬁcant algorithmic and modeling contributions) or papers that deal with engineering aspects of network design. Since the audience for this journal is then necessarily broad, articles that impact multiple application areas or that creatively use new or existing methodologies are especially appropriate. We seek to publish original, well-written research papers that make a substantive contribution to the knowledge base. In addition, tutorial and survey articles are welcomed. All manuscripts are carefully refereed.