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A Graph Theoretic Approach to Solve Special Knapsack Problems in Polynomial Time

In: Operations Research Proceedings 2017

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  • Carolin Rehs

    (Algorithmics for Hard Problems Group)

  • Frank Gurski

    (Algorithmics for Hard Problems Group)

Abstract

We introduce a graph theoretic approach in order to solve a large number of knapsack instances in polynomial time. For this purpose we apply threshold graphs, which have the useful property, that their independent sets correspond to feasible solutions in respective knapsack instances. We present a method to count and enumerate all maximal independent sets in a threshold graph in polynomial time and expanding this method for k-threshold graphs. This allows us to solve special knapsack instances as well as special multidimensional knapsack instances for a fixed number of dimensions in polynomial time. Furthermore, our results improve existing solutions for the maximum independent set problem on k-threshold graphs.

Suggested Citation

  • Carolin Rehs & Frank Gurski, 2018. "A Graph Theoretic Approach to Solve Special Knapsack Problems in Polynomial Time," Operations Research Proceedings, in: Natalia Kliewer & Jan Fabian Ehmke & Ralf Borndörfer (ed.), Operations Research Proceedings 2017, pages 295-301, Springer.
    • Handle: RePEc:spr:oprchp:978-3-319-89920-6_40
    DOI: 10.1007/978-3-319-89920-6_40
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    Cited by:

    1. Frank Gurski & Carolin Rehs, 2020. "Counting and enumerating independent sets with applications to combinatorial optimization problems," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 91(3), pages 439-463, June.

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