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We consider online scheduling on multiple machines for jobs arrivingone-by-one with the objective of minimizing the makespan. For any number ofidentical parallel or uniformly related machines, we provide acompetitive-ratio approximation scheme that computes an online algorithm whosecompetitive ratio is arbitrarily close to the best possible competitive ratio.We also determine this value up to any desired accuracy. This is the firstapplication of competitive-ratio approximation schemes in the online-listmodel. The result proves the applicability of the concept in different onlinemodels. We expect that it fosters further research on other online problems.

Competitive-Ratio Approximation Schemes for Minimizing the Makespan in the Online-List Model