Open AccessProceedings Article
Online Scheduling with Bounded Migration
Peter Sanders,Naveen Sivadasan,Martin Skutella +2 more
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TLDR
This work considers the classical online scheduling problem where jobs that arrive one by one are assigned to identical parallel machines with the objective of minimizing the makespan, and presents a linear time `online approximation scheme' that beats the lower bound on the performance of any online algorithm in the classical setting without migration.Abstract:
Consider the classical online scheduling problem where jobs that arrive one by one are assigned to identical parallel machines with the objective of minimizing the makespan. We generalize this problem by allowing the current assignment to be changed whenever a new job arrives, subject to the constraint that the total size of moved jobs is bounded by~$\beta$ times the size of the arriving job. Our main result is a linear time `online approximation scheme', that is, a family of online algorithms with competitive ratio~$1+\epsilon$ and constant migration factor~$\beta(\epsilon)$, for any fixed~$\epsilon>0$. This result is of particular importance if considered in the context of sensitivity analysis: While a newly arriving job may force a complete change of the entire structure of an optimal schedule, only very limited `local' changes suffice to preserve near-optimal solutions. We believe that this concept will find wide application in its own right. We also present simple deterministic online algorithms with migration factors~$\beta=2$ and~$\beta=4/3$, respectively. Their competitive ratio~$3/2$ beats the lower bound on the performance of any online algorithm in the classical setting without migration. We also present improved algorithms and similar results for closely related problems. In particular, there is a short discussion of corresponding results for the objective to maximize the minimum load of a machine. The latter problem has an application for configuring storage servers that was the original motivation for this work.read more
Citations
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Journal ArticleDOI
Online Scheduling with Bounded Migration
TL;DR: A linear time “online approximation scheme” is presented, that is, a family of online algorithms with competitive ratio arbitrarily close to 1 and constant migration factor, for small migration factors.
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Maintaining assignments online: matching, scheduling, and flows
TL;DR: This work shows that for edge-orientation, one can achieve a constant-competitive load while doing only a constant number of re-orientations per edge (in an amortized sense) and extend this to restricted machine scheduling with arbitrary sized jobs and give an algorithm that maintains load which is O(log log mn) times the optimum, and reassigns each job only an (amortized) constant amount of times.
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Online and Dynamic Algorithms for Set Cover
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Proceedings ArticleDOI
D-factor: a quantitative model of application slow-down in multi-resource shared systems
TL;DR: A general quantitative model for dilation factors of jobs in multi-resource systems is established and it is shown that the model can be integrated with an existing on-line scheduler to minimize the makespan of workloads.
References
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Book
Integer and Combinatorial Optimization
TL;DR: This chapter discusses the Scope of Integer and Combinatorial Optimization, as well as applications of Special-Purpose Algorithms and Matching.
Journal ArticleDOI
Using dual approximation algorithms for scheduling problems theoretical and practical results
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