Load Balancing: The Long Road from Theory to Practice

Sebastian Berndt, Max A. Deppert, Klaus Jansen, Lars Rohwedder


There is a long history of approximation schemes for the problem of scheduling jobs on identical machines to minimize the makespan. Such a scheme grants a (1+ϵ)-approximation solution for every ϵ>0, but the running time grows exponentially in 1/ϵ. For a long time, these schemes seemed like a purely theoretical concept. Even solving instances for moderate values of ϵ seemed completely illusional. In an effort to bridge theory and practice, we refine recent ILP techniques to develop the fastest known approximation scheme for this problem. An implementation of this algorithm reaches values of ϵ lower than 2/11≈18.2% within a reasonable timespan. This is the approximation guarantee of MULTIFIT, which, to the best of our knowledge, has the best proven guarantee of any non-scheme algorithm.
Original languageEnglish
Number of pages12
Publication statusPublished - 2022
EventSymposium on Algorithm Engineering and Experiments - Alexandria, United States
Duration: 09.01.202210.01.2022


ConferenceSymposium on Algorithm Engineering and Experiments
Abbreviated titleALENEX
Country/TerritoryUnited States

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