Load Balancing: The Long Road from Theory to Practice

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

doi:10.48550/ARXIV.2107.13638

Load Balancing: The Long Road from Theory to Practice

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

Institute of IT-Security

Abstract

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 language	English
Pages	104-116
Number of pages	12
DOIs	https://doi.org/10.48550/ARXIV.2107.13638
Publication status	Published - 2022
Event	Symposium on Algorithm Engineering and Experiments - Alexandria, United States Duration: 09.01.2022 → 10.01.2022

Conference

Conference	Symposium on Algorithm Engineering and Experiments
Abbreviated title	ALENEX
Country/Territory	United States
Period	09.01.22 → 10.01.22

UN SDGs

This output contributes to the following UN Sustainable Development Goals (SDGs)

Access to Document

10.48550/ARXIV.2107.13638

https://arxiv.org/abs/2107.13638

Cite this

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title = "Load Balancing: The Long Road from Theory to Practice",

abstract = "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. ",

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AU - Berndt, Sebastian

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AU - Jansen, Klaus

AU - Rohwedder, Lars

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N2 - 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.

AB - 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.

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T2 - Symposium on Algorithm Engineering and Experiments

Y2 - 9 January 2022 through 10 January 2022

ER -