Robust Scheduling on Uniform Machines -- New Results Using a Relaxed Approximation Guarantee
Hauke Brinkop, David Fischer, Klaus Jansen

TL;DR
This paper develops new efficient approximation schemes for online scheduling on uniform machines, balancing near-optimal solutions with limited job reassignments, extending prior results from identical to uniform machines.
Contribution
It introduces the first polynomial time approximation schemes for online scheduling with bounded reassignment on uniform machines, using novel rounding and machine division techniques.
Findings
EPTAS with load error $ ext{O}( extvarepsilon p_{ ext{max}})$ and constant migration factor.
EPAS algorithms parameterized by maximum processing time and number of distinct processing times.
First polynomial time approximation schemes for online scheduling with bounded reassignment on uniform machines.
Abstract
We consider the problem of scheduling jobs on uniform machines while minimizing the makespan () and maximizing the minimum completion time () in an online setting with migration of jobs. In this online setting, the jobs are inserted or deleted over time, and at each step, the goal is to compute a near-optimal solution while reassigning some jobs, such that the overall processing time of reassigned jobs, called migration, is bounded by some factor times the processing time of the job added or removed. We propose Efficient Polynomial Time Approximation Schemes (EPTASs) with an additional load error of for both problems, with constant amortized migration factor , where is the maximum processing time in the instance over all steps. As an intermediate step, we obtain Efficient Parameterized…
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Taxonomy
TopicsOptimization and Search Problems · Scheduling and Optimization Algorithms · Optimization and Packing Problems
