On the Value of Job Migration in Online Makespan Minimization
Susanne Albers, Matthias Hellwig

TL;DR
This paper investigates how limited job migration in online scheduling can improve makespan minimization, establishing optimal competitive ratios and migration bounds for deterministic algorithms on identical parallel machines.
Contribution
It introduces a deterministic online algorithm with proven competitive ratios using job migration, and provides matching lower bounds, advancing understanding of migration's impact.
Findings
Achieves an $oldsymbol{oldsymbol{ ext{α}_m}}$-competitive ratio with migration bounds.
Provides a lower bound showing no o(n) migration algorithm can do better.
Develops trade-off algorithms balancing competitiveness and migration count.
Abstract
Makespan minimization on identical parallel machines is a classical scheduling problem. We consider the online scenario where a sequence of jobs has to be scheduled non-preemptively on machines so as to minimize the maximum completion time of any job. The best competitive ratio that can be achieved by deterministic online algorithms is in the range . Currently no randomized online algorithm with a smaller competitiveness is known, for general . In this paper we explore the power of job migration, i.e.\ an online scheduler is allowed to perform a limited number of job reassignments. Migration is a common technique used in theory and practice to balance load in parallel processing environments. As our main result we settle the performance that can be achieved by deterministic online algorithms. We develop an algorithm that is -competitive, for any…
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Taxonomy
TopicsScheduling and Optimization Algorithms · Optimization and Search Problems · Distributed and Parallel Computing Systems
