Optimizing busy time on parallel machines

Mertzios, George B.; Shalom, Mordechai; Voloshin, Ariella; Wong, Prudence W. H.; Zaks, Shmuel

doi:10.1016/j.tcs.2014.10.033

Cited by 27 publications

(9 citation statements)

References 23 publications

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“…It was proved that the problem to minimize the total busy time is NP-hard for g ≥ 2 and a 4-competitive offline algorithm was proposed. George et al [21] considered two special instances: clique instances (the intervals of all jobs share a common time point) and proper instances (the intervals of all jobs are not contained in one another), and provided constant factor approximation algorithms. However, the interval scheduling problem differs from our problem because the ending time of a job is known at the time of its assignment in interval scheduling, whereas in our MinTotal DBP model, the departure time is not known at the time of item assignment.…”

Section: Related Workmentioning

confidence: 99%

On dynamic bin packing for resource allocation in the cloud

Tang

Cai

2014

Proceedings of the 26th ACM Symposium on Parallelism in Algorithms and Architectures

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Dynamic Bin Packing (DBP) is a variant of classical bin packing, which assumes that items may arrive and depart at arbitrary times. Existing works on DBP generally aim to minimize the maximum number of bins ever used in the packing. In this paper, we consider a new version of the DBP problem, namely, the MinTotal DBP problem which targets at minimizing the total cost of the bins used over time. It is motivated by the request dispatching problem arising in cloud gaming systems. We analyze the competitive ratios of the commonly used First Fit, Best Fit, and Any Fit packing (the family of packing algorithms that open a new bin only when no currently opened bin can accommodate the item to be packed) algorithms for the MinTotal DBP problem. We show that the competitive ratio of Any Fit packing cannot be better than the max/min item interval length ratio μ. The competitive ratio of Best Fit packing is not bounded for any given μ. For First Fit packing, if all the item sizes are smaller than W k (W is the bin capacity and k > 1 is a constant), it has a competitive ratio of k k−1 · μ+ 6k k−1 +1. For the general case, First Fit packing has a competitive ratio of 2μ + 13. We also propose a Modified First Fit packing algorithm that can achieve a competitive ratio of 8 7 μ + 55 7 when μ is not known and can achieve a competitive ratio of μ + 8 when μ is known.

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Section: Related Workmentioning

confidence: 99%

On dynamic bin packing for resource allocation in the cloud

Tang

Cai

2014

Proceedings of the 26th ACM Symposium on Parallelism in Algorithms and Architectures

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“…Mertzios et al [12] consider a dual problem to busy time minimization: the resource allocation maximization version. Here, the goal is to maximize the number of jobs scheduled without violating a budget constraint given in terms of busy time and the parallelism constraint.…”

Section: Related Workmentioning

confidence: 99%

LP rounding and combinatorial algorithms for minimizing active and busy time

Chang

Khuller

Mukherjee

2017

J Sched

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Abstract. We consider fundamental scheduling problems motivated by energy issues. In this framework, we are given a set of jobs, each with a release time, deadline and required processing length. The jobs need to be scheduled on a machine so that at most g jobs are active at any given time. The duration for which a machine is active (i.e., "on") is referred to as its active time. The goal is to find a feasible schedule for all jobs, minimizing the total active time. When preemption is allowed at integer time points, we show that a minimal feasible schedule already yields a 3-approximation (and this bound is tight) and we further improve this to a 2-approximation via LP rounding techniques. Our second contribution is for the non-preemptive version of this problem. However, since even asking if a feasible schedule on one machine exists is NP-hard, we allow for an unbounded number of virtual machines, each having capacity of g. This problem is known as the busy time problem in the literature and a 4-approximation is known for this problem. We develop a new combinatorial algorithm that gives a 3-approximation. Furthermore, we consider the preemptive busy time problem, giving a simple and exact greedy algorithm when unbounded parallelism is allowed, i.e., g is unbounded. For arbitrary g, this yields an algorithm that is 2-approximate.

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“…Gandhi et al [8] address the problem of allocating an available power budget among servers in a virtualized heterogeneous server farm, while minimizing the mean response time. Mertzios et al [17] have considered the problem of minimizing the power consumption of a set of machines which can be measured by the amount of time the machines are switched on and processing jobs. Specifically, the above work tries to consolidate jobs whose processing times overlap, such that to minimize the busy time of machines.…”

Section: Related Workmentioning

confidence: 99%

Application-Aware Workload Consolidation to Minimize Both Energy Consumption and Network Load in Cloud Environments

Tziritas

Loukopoulos

et al. 2013

2013 42nd International Conference on Parallel Processing

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Abstract-In this paper we tackle the problem of virtual machine (VM) placement onto physical servers to jointly optimize two objective functions. The first objective is to minimize the total energy spent within a cloud due to the servers that are commissioned to satisfy the computational demands of VMs. The second objective is to minimize the total network overhead incurred due to: (a) communicational dependencies between VMs, and (b) the VM migrations performed for the transition from an old assignment scheme to a new one. We study different methodologies for solving the aforementioned problem. The first approach is based on VM packing algorithms that optimize the above objective functions separately, reaching a single solution. The other approach is to tackle simultaneously the two optimization targets and define a set of non-dominating solutions. Performance evaluation using simulation experiments reveals interesting trade-offs between energy consumption and network load.

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Optimizing busy time on parallel machines

Cited by 27 publications

References 23 publications

On dynamic bin packing for resource allocation in the cloud

On dynamic bin packing for resource allocation in the cloud

LP rounding and combinatorial algorithms for minimizing active and busy time

Application-Aware Workload Consolidation to Minimize Both Energy Consumption and Network Load in Cloud Environments

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