Optimal online algorithms for scheduling on two identical machines under a grade of service

Jiang, Yiwei; He, Yong; Tang, Chunmei

doi:10.1631/jzus.2006.a0309

Cited by 62 publications

(21 citation statements)

References 7 publications

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“…Thus, there are several results with regard to cases that have a specific number of machines. Park et al (2006) and Jiang et al (2006) independently consider GoS eligibility with two machines. In both papers, the authors first show that any online algorithm must have a competitive ratio of at least 5/3 and then present an online algorithm with a competitive ratio of 5/3.…”

Section: Arbitrary Eligibilitymentioning

confidence: 99%

Makespan minimization in online scheduling with machine eligibility

2010

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In this paper we provide a survey of online scheduling in parallel machine environments with machine eligibility constraints and the makespan as objective function. We first give a brief overview of the different parallel machine environments and then survey the various types of machine eligibility constraints, including treehierarchical processing sets, Grade of Service processing sets, interval processing sets, and nested processing sets. We furthermore describe the relationships between the various different types of processing sets. We proceed with describing two basic online scheduling paradigms, namely online over list and online over time. For each one of the two paradigms we survey all the results that have been recorded in the literature with regard to each type of machine eligibility constraints. We obtain also

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Section: Arbitrary Eligibilitymentioning

confidence: 99%

Makespan minimization in online scheduling with machine eligibility

2010

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“…Park et al [11] and Jiang et al [9] independently presented an optimal algorithm with a competitive ratio of 5/3 for the integral model on two identical machines. When two machines have different speeds, Chassid and Epstein [4] proved the optimal algorithm has a competitive ratio 1+2s+s 2 1+s+s 2 for the fractional model, Tan and Zhang [12] proved the optimal algorithm has a competitive ratio of…”

Section: Introductionmentioning

confidence: 99%

A Mathematical Programming Approach for Online Hierarchical Scheduling

Tan

Zhang

2009

Combinatorial Optimization and Applications

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Abstract. This paper considers an online hierarchical scheduling problem on parallel identical machines. We are given a set of m machines and a sequence of jobs. Each machine has a different hierarchy, and each job also has a hierarchy associated with it. A job can be assigned to a machine only if its hierarchy is no less than that of the machine. The objective is to minimize makespan. Two models are studied in the paper. For the fractional model, we present an improved algorithm and lower bounds. Both algorithm and lower bounds are based on solutions of mathematical programming. For any given m, our algorithm is optimal by numerical calculation. For the integral model, we present both a general algorithm for any m, and an improved algorithm with better competitive ratios of 2.333 and 2.610 for m = 4 and 5, respectively.

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“…Park, Chang and Lee [13] and independently Jiang, He and Tang [12] studied the problem on two identical speed hierarchical machines. They both designed 5 3 -competitive algorithms and showed that this ratio is best possible.…”

Section: Introductionmentioning

confidence: 99%

“…The authors further showed that this is best possible. The paper [12] considered a restricted type of a preemptive model in which idle time is not allowed. They designed a 3 2 -competitive algorithm and showed this is best possible.…”

Section: Introductionmentioning

confidence: 99%

The hierarchical model for load balancing on two machines

Chassid

Epstein

2007

J Comb Optim

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Following previous work, we consider the hierarchical load balancing model on two machines of possibly different speeds. We first focus on maximizing the minimum machine load and show that no competitive algorithm exists for this problem. We overcome this barrier in two ways, both related to previously known models. The first one is fractional assignment, where each job can be arbitrarily split between the machines. The second one is a semi-online model where the sum of jobs is known in advance. We design algorithms of best possible competitive ratios for both these cases. Furthermore, we show that the combination of the two models leads to the existence of an optimal algorithm (i.e., an algorithm of competitive ratio 1). This algorithm is clearly optimal for the makespan minimization problem as well. For the latter problem, we consider the fractional assignment model and design an algorithm of best possible competitive ratio for it.

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Optimal online algorithms for scheduling on two identical machines under a grade of service

Cited by 62 publications

References 7 publications

Makespan minimization in online scheduling with machine eligibility

Makespan minimization in online scheduling with machine eligibility

A Mathematical Programming Approach for Online Hierarchical Scheduling

The hierarchical model for load balancing on two machines

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