Network flows: theory, algorithms, and applications
Network flows: theory, algorithms, and applications
Sensitivity analysis of list scheduling heuristics
Discrete Applied Mathematics
Approximation in stochastic scheduling: the power of LP-based priority policies
Journal of the ACM (JACM)
On randomized online scheduling
STOC '02 Proceedings of the thiry-fourth annual ACM symposium on Theory of computing
Developments from a June 1996 seminar on Online algorithms: the state of the art
Sensitivity Analysis for Scheduling Problems
Journal of Scheduling
An exact algorithm for the robust shortest path problem with interval data
Computers and Operations Research
Sensitivity bounds for machine scheduling with uncertain communication delays
Journal of Scheduling
A new average case analysis for completion time scheduling
Journal of the ACM (JACM)
Models and Algorithms for Stochastic Online Scheduling
Mathematics of Operations Research
Average-Case and Smoothed Competitive Analysis of the Multilevel Feedback Algorithm
Mathematics of Operations Research
Scheduling: Theory, Algorithms, and Systems
Scheduling: Theory, Algorithms, and Systems
An approximation algorithm for interval data minmax regret combinatorial optimization problems
Information Processing Letters
Robust optimization in the presence of uncertainty
Proceedings of the 4th conference on Innovations in Theoretical Computer Science
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While standard parallel machine scheduling is concerned with good assignments of jobs to machines, we aim to understand how the quality of an assignment is affected if the jobs' processing times are perturbed and therefore turn out to be longer (or shorter) than declared. We focus on online scheduling with perturbations occurring at any time, such as in railway systems when trains are late. For a variety of conditions on the severity of perturbations, we present bounds on the worst case ratio of two makespans. For the first makespan, we let the online algorithm assign jobs to machines, based on the non-perturbed processing times. We compute the makespan by replacing each job's processing time with its perturbed version while still sticking to the computed assignment. The second is an optimal offline solution for the perturbed processing times. The deviation of this ratio from the competitive ratio of the online algorithm tells us about the "price of perturbations". We analyze this setting for Graham's algorithm, and among other bounds show a competitive ratio of 2 for perturbations decreasing the processing time of a job arbitrarily, and a competitive ratio of less than 2.5 for perturbations doubling the processing time of a job. We complement these results by providing lower bounds for any online algorithm in this setting. Finally, we propose a risk-aware online algorithm tailored for the possible bounded increase of the processing time of one job, and we show that this algorithm can be worse than Graham's algorithm in some cases.