Performance Guarantees of Local Search for Multiprocessor Scheduling

Schuurman, Petra; Vredeveld, Tjark

doi:10.1287/ijoc.1050.0152

Cited by 67 publications

(47 citation statements)

References 31 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…PROPOSITION 2.1: (Finn and Horowitz [5]; Schuurman and Vredeveld [17]) The worst‐case performance guarantee of any jump‐optimal schedule and of any lex‐jump‐optimal schedule for P || C max is 2 ‐ 2/( m + 1) . This bound is tight for both neighborhoods.…”

Section: Preliminaries On Schedules and Neighborhoodsmentioning

confidence: 99%

“…A natural neighborhood for our scheduling problem P || C max is the so‐called jump neighborhood; in this jump neighborhood schedule σ ′ is a neighbor of schedule σ , if σ ′ results from σ by moving a single job from one machine to another machine. Finn and Horowitz [5] showed that a local optimum with respect to the jump neighborhood has a performance guarantee of 2 ‐ 2/( m + 1), and Schuurman and Vredeveld [17] showed that this bound is tight. The number of moves needed to find a jump‐optimal solution by means of an iterative improvement procedure is \documentclass{article} \usepackage{mathrsfs} \usepackage{amsmath, amssymb} \pagestyle{empty} \begin{document} \begin{align*}\mathcal{O}(n^2)\end{align*} \end{document} (as shown by Brucker et al [3]) and there exist instances for which this bound is asymptotically tight (as shown by Hurkens and Vredeveld [12]).…”

Section: Introductionmentioning

confidence: 99%

“…These neighborhoods allow us to make simultaneous cyclic exchanges of jobs between appropriately chosen subsets of the machines, and they both have exponential size. One drawback of these neighborhoods is that deciding the existence of an improving neighbor is NP‐complete [6], and another drawback is that the performance guarantees of their local optima do not improve upon the guarantees for the jump neighborhood (as shown by Schuurman and Vredeveld [17]).…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Exponential size neighborhoods for makespan minimization scheduling

Brueggemann¹,

Hurink²,

Vredeveld³

et al. 2011

Naval Research Logistics

Self Cite

View full text Add to dashboard Cite

Abstract:We investigate the quality of local search heuristics for the scheduling problem of minimizing the makespan on identical parallel machines. We study exponential size neighborhoods (whose size grows exponentially with the input length) that can be searched in polynomial time, and we derive worst-case approximation guarantees for the local optima of such neighborhoods. The so-called split neighborhood splits a feasible schedule into two layers, and then recombines the two layers by finding a perfect matching. We show that the makespan of every local optimum for split is at most a factor of 2 away from the globally optimal makespan. We then combine the split neighborhood with two neighborhoods from the literature. The combination of split with the jump neighborhood only marginally improves the approximation guarantee, whereas the combination with the lexicographicjump neighborhood decreases the approximation guarantee from 2 to 3/2.

show abstract

Section: Preliminaries On Schedules and Neighborhoodsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Exponential size neighborhoods for makespan minimization scheduling

Brueggemann¹,

Hurink²,

Vredeveld³

et al. 2011

Naval Research Logistics

Self Cite

View full text Add to dashboard Cite

show abstract

“…The price of anarchy for sequencing models when SPT policy is used is: -2 − 2/(m + 1) for m identical machines [19], -Θ(log m) for m related (restricted) machines [14], at most m for m unrelated machines [14].…”

Section: Related Workmentioning

confidence: 99%

“…The result in [14] is derived from the bound for the classical Ibarra-Kim algorithm which produces a locally optimum solution for the scheduling problem [19]. We like to point out that tere is a subtle but important difference between a locally optimal solution and a Nash solution.…”

Section: Corollary 11 the Price Of Stability In Scheduling Games Witmentioning

confidence: 99%

The price of stability in selfish scheduling games

Agussurja

Lau

2009

Web Intelligence and Agent Systems: An International Journal

View full text Add to dashboard Cite

Game theory has gained popularity as an approach to analysing and understanding distributed systems with selfinterested agents. Central to game theory is the concept of Nash equilibrium as a stable state (solution) of the system, which comes with a price − the loss in efficiency. The quantification of the efficiency loss is one of the main research concerns. In this paper, we study the quality and computational characteristics of the best Nash equilibrium in two selfish scheduling models: the congestion model and the sequencing model. In particular, we present the following results: (1) In the congestion model: first, the best Nash equilibrium is socially optimum and consequently, computing the best Nash is NP-hard; second, any -approximation algorithm for finding the optimum can be transformed into an -approximation algorithm for the best Nash. (2) In sequencing model: for identical machines, we show that the best Nash is no better than the worst Nash and it is easy to compute; for related machines, we show that there is a gap between the worst and the best Nash equilibrium, and leave the analytical bound of this gap for future work.

show abstract

Coordination mechanisms for decentralized parallel systems

Cohen

Cordeiro

Trystram

2014

Concurrency and Computation

View full text Add to dashboard Cite

International audienceOn resource sharing platforms, the execution of the jobs submitted by users is usually controlled by a centralized global scheduler. It determines efficient schedules regarding some common objective function that all organizations agree with (for instance, maximizing the utilization of the entire platform). However, in practice, each organization is mostly interested in the performance obtained for its own jobs. We study the price that the collectivity must pay in order to allow independence to selfish, self-governing organizations, so they can choose the best schedules for their own jobs. In other words, we are interested in analyzing the costs on the global performance inflicted by the decentralization of scheduling policies. We present a game-theoretic model for the problem and the associated coordination mechanisms developed to reduce the cost of the decentralization of the decision-making process. The main contribution is to show (in theory and practice) how to devise pure Nash equilibria configurations for every instance of the problem and to prove that the price paid by the collectivity depends on the local scheduling policy and on the characteristics of the workload executed on such platform

show abstract

Performance Guarantees of Local Search for Multiprocessor Scheduling

Cited by 67 publications

References 31 publications

Exponential size neighborhoods for makespan minimization scheduling

Exponential size neighborhoods for makespan minimization scheduling

The price of stability in selfish scheduling games

Coordination mechanisms for decentralized parallel systems

Contact Info

Product

Resources

About