Online Makespan Scheduling with Job Migration on Uniform Machines

Abstract In the classic minimum makespan scheduling problem, we are given an input sequence of n jobs with sizes. A algorithm has to assign m parallel machines. The objective is minimize makespan, which time it takes until all processed. this paper, consider online algorithms without preemption. However, allow change assignment up k at end for some limited number . For identical machines, Albers and Hellwig (Algorithmica 79(2):598–623, 2017) give tight bounds on competitive ratio in model. precise depends on, increases with, It lies between 4/3 $$\approx 1.4659$$ ≈ 1.4659 They show that $$k = O(m)$$ k = O ( m ) sufficient achieve bound no o(n)$$ o n can result a better bound. We study uniform i.e., machines different speeds, setting strictly harder. sufficiently large , there $$\delta \varTheta (1)$$ δ Θ 1 such that, only two machine less than $$1.4659 + \delta $$ + present new setting. Depending speeds our achieves 1.7992$$ 1.7992 also \varOmega (m)$$ Ω necessary below 2. Our based maintaining specific imbalance respect completion times complemented by bicriteria approximation minimizes maximizes average certain sets