Online optimization of busy time on parallel machines

Shalom, Mordechai; Voloshin, Ariella; Wong, Prudence W. H.; Yung, Fencol C. C.; Zaks, Shmuel

doi:10.1016/j.tcs.2014.07.017

Cited by 25 publications

(14 citation statements)

References 9 publications

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“…For example, Lin et al [6] transforms the bi-objectives problem of energy cost minimization and the QoS maximization to a single objective problem with a tradeoff parameter λ. Gupta et al, [31] models the workload as workflow graphs with task dependencies, and aims to design scheduling strategies by considering tasks dependencies and their deadlines while maximizing the energy efficiency. Wong et al [46] studies the schedule that at most g jobs can be running on each machine at any given time to minimize the total active time. Shachnai et al [35] aims to minimize the number of active time units of multiple machines to reduce the power consumption.…”

Section: B Qos-aware Vm Schedulingmentioning

confidence: 99%

Electricity Price-aware Consolidation Algorithms for Time-sensitive VM Services in Cloud Systems

Wang

Fang

et al. 2021

IEEE Trans. Serv. Comput.

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Despite the salient feature of cloud computing, the cloud provider still suffers from electricity bill, which in part comes from 1) the power consumption of running physical machines (PMs) to guarantee the resource/time requirements of virtual machines (VMs), and 2) the dynamically varying electricity price offered by smart grids. In the literature, there exist viable solutions adaptive to electricity price variation to reduce the electricity bill. However, they are not applicable to serving time-sensitive VM requests. In serving time-sensitive VM requests, it is potential for the cloud provider to apply proper consolidation strategies to further reduce the electricity bill. Few prior works have provided theoretical solutions of VM consolidation strategies that are adaptive to electricity price variations in serving time-sensitive VM requests. In this work, to address this challenge, we develop electricity-priceaware consolidation algorithms for both the offline and online scenarios. For the offline scenario, we first develop a consolidation algorithm with constant approximation, which always approaches the optimal solution within a constant factor of 5. For the online scenario, we propose an O(log( Lmax L min ))-competitive algorithm that is able to approach the optimal offline solution within a logarithmic factor, where Lmax L min is the ratio of the longest length of the processing time requirement of VMs to the shortest one. Our trace-driven simulation results further demonstrate that the average performance of the proposed algorithms produce nearoptimal electricity bill.

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Section: B Qos-aware Vm Schedulingmentioning

confidence: 99%

Electricity Price-aware Consolidation Algorithms for Time-sensitive VM Services in Cloud Systems

Wang

Fang

et al. 2021

IEEE Trans. Serv. Comput.

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“…Generalizations considered include minimizing the sum of the colors assigned to the vertices [11,12,15,19]; incorporating a bandwidth requirement for each interval and allowing overlapping intervals to be assigned the same color as long as their total bandwidth requirement does not exceed the capacity [1,3]. The work most relevant to this paper includes generalized coloring problems studied in [2,17,23] and the busy time scheduling problems [5,6,8,13,18,22].…”

Section: Introductionmentioning

confidence: 99%

“…A 2-approximation algorithm is also proposed in the paper. In the busy time scheduling problem [5,6,8,13,18,22], a machine (cf. color) can be shared by a certain number of jobs (cf.…”

Section: Introductionmentioning

confidence: 99%

Complexity and online algorithms for minimum skyline coloring of intervals

Erlebach

Liu

et al. 2019

Theoretical Computer Science

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Graph coloring has been studied extensively in the literature. The classical problem concerns the number of colors used. In this paper, we focus on coloring intervals where the input is a set of intervals and two overlapping intervals cannot be assigned the same color. In particular, we are interested in the setting where there is an increasing cost associated with using a higher color index. Given a set of intervals (on a line) and a coloring, the cost of the coloring at any point is the cost of the maximum color index used at that point and the cost of the overall coloring is the integral of the cost over all points on the line. The objective is to assign a valid color to each interval and minimize the total cost of the coloring. Intuitively, the maximum color index used at each point forms a skyline and so the objective is to obtain a minimum skyline coloring. The problem arises in various applications including optical networks and job scheduling. Alicherry and Bhatia defined in 2003 a more general problem in which the colors are partitioned into classes and the cost of a color depends solely on its class. This problem is NP-hard and the reduction relies on the fact that some color class has more than one color. In this paper we show that when each color class only contains one color, this simpler setting remains NP-hard via a reduction from the arc coloring problem. In addition, we initiate the study of the online setting and present an asymptotically optimal online algorithm. We further study a variant of the problem in which the intervals are already partitioned into sets and the objective is to assign a color to each set such that the total cost is minimum. We show that this seemingly easier problem remains NP-hard by a reduction from the optimal linear arrangement problem.

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“…For the interval job scheduling problem with bounded parallelism, Shalom et al [70] derived a lower bound of g on the competitive ratio of any deterministic online algorithm,…”

Section: A Lower Bound On Competitiveness Of Any Deterministic Onlinementioning

confidence: 99%

“…This lower bound is not applicable to our MinUsageTime DBP problem because items can have arbitrary sizes in our problem so that the maximum number of items that can be placed in a bin is not fixed. Inspired by the study of [70], we construct a new instance to bound the competitive ratio of any deterministic online packing algorithm by a function of the max/min item duration ratio µ. Our instance also uses items with the same size 1 k such that each bin can accommodate at most k items at any moment.…”

Section: A Lower Bound On Competitiveness Of Any Deterministic Onlinementioning

confidence: 99%

Combinatorial algorithms for scheduling jobs to minimize server usage time

Ren¹

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This thesis is concerned with three combinatorial optimization problems for job scheduling, named the MinUsageTime Dynamic Bin Packing problem, the Energy-Efficient Job Scheduling problem and the Flexible Job Scheduling problem. These problems are motivated by emerging issues arising from cloud computing and energy-efficient computing. A central theme of these problems is to minimize the server usage time for processing jobs. In this thesis, we focus on the algorithmic aspects of each problem by proposing online and approximation algorithms in the online and offline settings respectively.

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Online optimization of busy time on parallel machines

Cited by 25 publications

References 9 publications

Electricity Price-aware Consolidation Algorithms for Time-sensitive VM Services in Cloud Systems

Electricity Price-aware Consolidation Algorithms for Time-sensitive VM Services in Cloud Systems

Complexity and online algorithms for minimum skyline coloring of intervals

Combinatorial algorithms for scheduling jobs to minimize server usage time

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