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AnO (n)-algorithm for LP-knapsacks with a fixed number of GUB constraints

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Abstract

AnO (n+r logn) algorithm is presented for the linear programming knapsack problem withr generalized upper bounds andn variables. This result which is based on parametric programming and well-known ideas for the design of linear-time algorithms improvesO (n logn) algorithms given byGlover/Klingman [1979] andZemel [1980].

Zusammenfassung

Es wird einO (n+r logn)-Algorithmus vorgestellt, der LP-Rucksackprobleme mitn Variablen undr verallgemeinerten oberen Schranken für die Variablen löst. Grundlage des Verfahrens ist ein parametrischer Ansatz kombiniert mit bekannten Methoden zur Konstruktion von Algorithmen mit linearer Laufzeit. Der vorgestellte Algorithmus verbessertO (n logn)-Verfahren vonGlover/Klingman [1979] undZemel [1980].

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Authors and Affiliations

  1. FB Mathematik, Universität Osnabrück, Postfach 4469, D-4500, Osnabrück

    P. Brucker

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  1. P. Brucker
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Brucker, P. AnO (n)-algorithm for LP-knapsacks with a fixed number of GUB constraints. Zeitschrift für Operations Research 28, 29–40 (1984). https://doi.org/10.1007/BF01919085

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  • DOI: https://doi.org/10.1007/BF01919085

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