Lower bounds for online scheduling on four processors

O. Braun (), F. Chung () and R. L. Graham
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O. Braun: University of California, San Diego
F. Chung: University of California, San Diego
R. L. Graham: University of California, San Diego

Journal of Scheduling, 2025, vol. 28, issue 5, No 4, 529-544

Abstract: Abstract We explore lower bounds concerning the makespan of any online scheduling algorithm for the parallel processor scheduling problem with four processors. We prove that any online algorithm exhibits a makespan of at least $$\sqrt{3}$$ 3 times that of an optimal offline schedule, minus an additional constant of $$2-\sqrt{3}$$ 2 - 3 , thus yielding an asymptotic competitive ratio of $$\sqrt{3}$$ 3 . Moreover, specific absolute competitive ratios $$\sqrt{3}-\epsilon _r$$ 3 - ϵ r , where $$\epsilon _r>0$$ ϵ r > 0 depends on the number of tasks that have to be scheduled, are established for scenarios involving a finite number of tasks.

Keywords: Online scheduling; Parallel processors; Makespan; Competitive analysis; Lower bounds (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1007/s10951-025-00843-2

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