Online Hierarchical Scheduling on Two Uniform Machines with Bounded Job Sizes

2015 ◽  
Vol 32 (05) ◽  
pp. 1550032 ◽  
Author(s):  
Xinrong Lu ◽  
Zhaohui Liu
Keyword(s):  
Speed Ratio ◽  
Scheduling Problem ◽  
Optimal Algorithms ◽  
Hierarchical Scheduling ◽  
Uniform Machines

This paper studies the online hierarchical scheduling problem on two uniform machines with bounded job sizes, where the first machine M1 receives both low and high hierarchy jobs, while the second machine M2 only receives high hierarchy jobs. The machines have a speed ratio of s(s ≥ 1), and M2 runs faster. Jobs are revealed one by one, and before the current job is scheduled, we have no information about next jobs except that the size of any job is in the interval [1, t]. The objective is to minimize the makespan. We present optimal algorithms for all (s, t) pairs.

OPTIMAL PREEMPTIVE SEMI-ONLINE ALGORITHM FOR SCHEDULING TIGHTLY-GROUPED JOBS ON TWO UNIFORM MACHINES

2006 ◽  
Vol 23 (01) ◽  
pp. 77-88 ◽  
Author(s):  
YIWEI JIANG ◽  
YONG HE
Keyword(s):  
Online Algorithm ◽  
Size Ratio ◽  
Speed Ratio ◽  
Preemptive Scheduling ◽  
Scheduling Problem ◽  
Time Zero ◽  
Uniform Machines ◽  
Machine Speed

In this paper, we consider a semi-online preemptive scheduling problem on two uniform machines, where we assume that all jobs have sizes between p and rp for some p > 0 and r ≥ 1. The goal is to maximize the continuous period of time (starting from time zero) when both machines are busy. We present an optimal semi-online algorithm for any combination of the job size ratio r and machine speed ratio s.

Online Preemptive Hierarchical Scheduling on Two Uniform Machines with Rejection

2015 ◽  
Vol 32 (04) ◽  
pp. 1550027
Author(s):  
Xiao Min ◽  
Jing Liu ◽  
Yanxia Dong ◽  
Ming Jiang
Keyword(s):  
Lower Bound ◽  
Online Algorithms ◽  
Upper Bound ◽  
Competitive Ratio ◽  
Scheduling Problem ◽  
Hierarchical Scheduling ◽  
Uniform Machines ◽  
Level 1

This paper studies the online hierarchical scheduling problem on two uniform machines with rejection. Two uniform machines M1, M2 run at the speeds of s ∈ (0, +∞), 1 separately; and they are provided with different capabilities. Each machine has a certain GOS level 1 or 2 and every job is also associated with a hierarchy 1 or 2. The job can only be assigned to the machine whose GOS level does not exceed the job's hierarchy. Preemption is permitted but idle is not introduced. Jobs come one by one over list. When a job arrives, it can be accepted and scheduled on some machine or rejected by paying its penalty. The objective is to minimize the sum of makespan yielded by accepted jobs and total penalties of all rejected jobs. For this problem, we propose a family of several online algorithms according to the range of s and the related lower bound is also obtained. These algorithms achieve optimal competitive ratio when s ∈ (0, 1) ∪ [1.618, +∞), but have a small gap between upper bound and lower bound in interval [1, 1.618).

scholarly journals Optimal algorithms for the batch scheduling problem in OBS networks

2012 ◽  
Vol 56 (14) ◽  
pp. 3274-3286 ◽  
Author(s):  
Gustavo B. Figueiredo ◽  
Eduardo Candido Xavier ◽  
Nelson L.S. da Fonseca
Keyword(s):  
Batch Scheduling ◽  
Scheduling Problem ◽  
Optimal Algorithms

SEMI-ON-LINE SCHEDULING PROBLEM FOR MAXIMIZING THE MINIMUM MACHINE COMPLETION TIME ON THREE SPECIAL UNIFORM MACHINES

2005 ◽  
Vol 22 (02) ◽  
pp. 229-237 ◽  
Author(s):  
RUN-ZI LUO ◽  
SHI-JIE SUN
Keyword(s):  
Competitive Ratio ◽  
Completion Time ◽  
Processing Time ◽  
Scheduling Problem ◽  
Uniform Machines ◽  
On Line ◽  
Special Case

In this paper, we investigate a semi-on-line version for a special case of three machines M1, M2, M3 where the processing time of the largest job is known in advance. A speed si(s1 = s2 = 1, 1 ≤ s3 = s) is associated with machine Mi. Our goal is to maximize the C min — the minimum workload of three machines. We give a C min 3 algorithm and prove its competitive ratio is [Formula: see text] and the algorithm is the best possible for 1 ≤ s ≤ 2. We also claim the competitive ratio of algorithm C min 3 is tight.

scholarly journals Power Efficient Hierarchical Scheduling for DSP Transformations

VLSI Design ◽  
2002 ◽  
Vol 14 (2) ◽  
pp. 203-217
Author(s):  
P. K. Merakos ◽  
K. Masselos ◽  
C. E. Goutis
Keyword(s):  
Travelling Salesman Problem ◽  
Optimization Algorithms ◽  
Digital Signal ◽  
Scheduling Problem ◽  
Switching Activity ◽  
Travelling Salesman ◽  
Hierarchical Scheduling ◽  
Power Efficient ◽  
Target Architecture ◽  
Selection For

In this paper, the problem of scheduling the computation of partial products in transformational Digital Signal Processing (DSP) algorithms, aiming at the minimization of the switching activity in data and address buses, is addressed. The problem is stated as a hierarchical scheduling problem. Two different optimization algorithms, which are based on the Travelling Salesman Problem (TSP), are defined. The proposed optimization algorithms are independent on the target architecture and can be adapted to take into account it. Experimental results obtained from the application of the proposed algorithms in various widely used DSP transformations, like Discrete Cosine Transform (DCT) and Discrete Fourier Transform (DFT), show that significant switching activity savings in data and address buses can be achieved, resulting in corresponding power savings. In addition, the differences between the two proposed methods are underlined, providing envisage for their suitable selection for implementation, in particular transformational algorithms and architectures.

scholarly journals A Competitive Online Algorithm for Minimizing Total Weighted Completion Time on Uniform Machines

2020 ◽  
Vol 2020 ◽  
pp. 1-9
Author(s):  
Xuyang Chu ◽  
Jiping Tao
Keyword(s):  
Completion Time ◽  
Online Algorithm ◽  
Total Weighted Completion Time ◽  
Scheduling Problem ◽  
Uniform Machines ◽  
Online Setting ◽  
Weighted Completion Time ◽  
Waiting Strategy ◽  
Machine Speed ◽  
Over Time

We consider the classic online scheduling problem on m uniform machines in the online setting where jobs arrive over time. Preemption is not allowed. The objective is to minimize total weighted completion time. An online algorithm based on the directly waiting strategy is proposed. Its competitive performance is proved to be max2smax1−1/2∑si,2smax/1+smax2.5−1/2m by the idea of instance reduction, where sm is the fastest machine speed after being normalized by the slowest machine speed.

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