Nonclairvoyantly scheduling power-heterogeneous processors

Gupta, Anupam; Krishnaswamy, Ravishankar; Pruhs, Kirk

doi:10.1109/greencomp.2010.5598311

Cited by 10 publications

(15 citation statements)

References 25 publications

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“…When machine i uses power P > 0, it runs f −1 i (P ) times faster than its original speedit processes job j at a rate of ℓ ij f −1 i (P ). This model is widely studied [1,7,21,11,20,15] and we consider the standard objective of minimizing the total weighted flow-time plus the total energy consumption [2]. The same guarantee on the number of migrations by a job stated in Theorem 1.1 holds for this setting.…”

Section: Our Resultsmentioning

confidence: 99%

“…As mentioned above, the algorithmic idea based on coordination games is very different from the previous greedy dispatch rules [11,3,15] for clairvoyant scheduling, and also from previous work on non-clairvoyant scheduling [21,20,25]. We contrast our algorithm with these, highlighting the necessity of new techniques.…”

Section: Comparison With Previous Techniquesmentioning

confidence: 98%

“…This difficulty appears in the two analysis tools for online scheduling, potential function [27] and dual fitting method [3,23,15]. Due to these difficulties, there have been very few results for non-clairvoyant scheduling on heterogeneous machines [21,20,25]. Further, there has been no work in any heterogeneous machines setting for the weighted flow-time objective.…”

Section: Technical Contributions: Selfish Migration and Nash Equilibriummentioning

confidence: 99%

“…Each machine maintains a virtual queue on the current set of jobs assigned to it; newly arriving jobs are appended to the tail of this queue. In a significant departure from previous work [3,15,21,20,25], each machine treats a migration of a job to it as an arrival, and a migration out of it as a departure. This means a job migrating to a machine is placed at the tail of the virtual queue.…”

Section: Selfishmigrate Frameworkmentioning

confidence: 99%

“…The simplicity makes the framework extend easily to energy constraints. The resulting accounting using the delay a job j induces to those ahead of it in its virtual queue is novel -in contrast to previous work [3,15,21,20,25], the virtual queue changes with time and could possibly include jobs whose original arrival time r j ′ is later than that of job j.…”

Section: Comparison With Previous Techniquesmentioning

confidence: 99%

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SelfishMigrate: A Scalable Algorithm for Non-clairvoyantly Scheduling Heterogeneous Processors

Kulkarni

Munagala

et al. 2014

2014 IEEE 55th Annual Symposium on Foundations of Computer Science

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We consider the classical problem of minimizing the total weighted flow-time for unrelated machines in the online non-clairvoyant setting. In this problem, a set of jobs J arrive over time to be scheduled on a set of M machines. Each job j has processing length p j , weight w j , and is processed at a rate of ℓ ij when scheduled on machine i. The online scheduler knows the values of w j and ℓ ij upon arrival of the job, but is not aware of the quantity p j . We present the first online algorithm that is scalable ((1 + ǫ)-speed O( 1 ǫ 2 )-competitive for any constant ǫ > 0) for the total weighted flow-time objective. No non-trivial results were known for this setting, except for the most basic case of identical machines. Our result resolves a major open problem in online scheduling theory. Moreover, we also show that no job needs more than a logarithmic number of migrations.We further extend our result and give a scalable algorithm for the objective of minimizing total weighted flow-time plus energy cost for the case of unrelated machines. In this problem, each machine can be sped up by a factor of f −1 i (P ) when consuming power P , where f i is an arbitrary strictly convex power function. In particular, we get an O(γ 2 )-competitive algorithm when all power functions are of form s γ . These are the first non-trivial non-clairvoyant results in any setting with heterogeneous machines.The key algorithmic idea is to let jobs migrate selfishly until they converge to an equilibrium. Towards this end, we define a game where each job's utility which is closely tied to the instantaneous increase in the objective the job is responsible for, and each machine declares a policy that assigns priorities to jobs based on when they migrate to it, and the execution speeds. This has a spirit similar to coordination mechanisms that attempt to achieve near optimum welfare in the presence of selfish agents (jobs). To the best our knowledge, this is the first work that demonstrates the usefulness of ideas from coordination mechanisms and Nash equilibria for designing and analyzing online algorithms.

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Section: Our Resultsmentioning

confidence: 99%

Section: Comparison With Previous Techniquesmentioning

confidence: 98%

Section: Technical Contributions: Selfish Migration and Nash Equilibriummentioning

confidence: 99%

Section: Selfishmigrate Frameworkmentioning

confidence: 99%

Section: Comparison With Previous Techniquesmentioning

confidence: 99%

See 3 more Smart Citations

SelfishMigrate: A Scalable Algorithm for Non-clairvoyantly Scheduling Heterogeneous Processors

Kulkarni

Munagala

et al. 2014

2014 IEEE 55th Annual Symposium on Foundations of Computer Science

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Managing Power Heterogeneity

Pruhs

2011

Theory and Practice of Algorithms in (Computer) Systems

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Primal-Dual and Dual-Fitting Analysis of Online Scheduling Algorithms for Generalized Flow Time Problems

Angelopoulos

Lucarelli

Nguyen

2015

Algorithms - ESA 2015

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We study online scheduling problems on a single processor that can be viewed as extensions of the well-studied problem of minimizing total weighted flow time. In particular, we provide a framework of analysis that is derived by duality properties, does not rely on potential functions and is applicable to a variety of scheduling problems. A key ingredient in our approach is bypassing the need for "black-box" rounding of fractional solutions, which yields improved competitive ratios.We begin with an interpretation of Highest-Density-First (HDF) as a primal-dual algorithm, and a corresponding proof that HDF is optimal for total fractional weighted flow time (and thus scalable for the integral objective). Building upon the salient ideas of the proof, we show how to apply and extend this analysis to the more general problem of minimizing j w j g(F j ), where w j is the job weight, F j is the flow time and g is a non-decreasing cost function. Among other results, we present improved competitive ratios for the setting in which g is a concave function, and the setting of same-density jobs but general cost functions. We further apply our framework of analysis to online weighted completion time with general cost functions as well as scheduling under polyhedral constraints.

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Nonclairvoyantly scheduling power-heterogeneous processors

Abstract: Abstract-We show that a natural nonclairvoyant online algorithm for scheduling jobs on a power-heterogeneous multiprocessor is bounded-speed bounded-competitive for the objective of flow plus energy.

Cited by 10 publications

References 25 publications

SelfishMigrate: A Scalable Algorithm for Non-clairvoyantly Scheduling Heterogeneous Processors

SelfishMigrate: A Scalable Algorithm for Non-clairvoyantly Scheduling Heterogeneous Processors

Managing Power Heterogeneity

Primal-Dual and Dual-Fitting Analysis of Online Scheduling Algorithms for Generalized Flow Time Problems

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