The quadratic 0-1 knapsack problem with series-parallel support

Authors:
David J. Rader Jr.;Gerhard J. Woeginger
Affiliations:
Department of Mathematics, Rose-Hulman Institute of Technology, Terre Haute, IN 47803, USA;Faculty of Mathematics, University of Twente, P.O. Box 217, 7500 AE Enschede, The Netherlands
Venue:
Operations Research Letters
Year:
2002

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Abstract

We consider various special cases of the quadratic 0-1 knapsack problem (QKP) for which the underlying graph structure is fairly simple. For the variant with edge series-parallel graphs, we give a dynamic programming algorithm with pseudo-polynomial time complexity, and a fully polynomial time approximation scheme. In strong contrast to this, the variant with vertex series-parallel graphs is shown to be strongly NP-complete.