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https://www.sciencedirect.com/science/article/pii/S0167637702001220
The special case of the QKP where E=∅ is the classical knapsack problem. Hence, QKP is an NP-hard problem. The special case of the QKP where c ij ⩾0 holds for all quadratic coefficients is the so-called supermodular knapsack problem. QKP has been used to model selection problems in telecommunications as well as compiler design problems .Cited by: 59
https://www.researchgate.net/publication/222196732_The_quadratic_0-1_knapsack_problem_with_series-parallel_support
The 0-1 quadratic knapsack problem (QKP) is a hard computational problem, which is a generalization of the knapsack problem (KP). In this paper, a mini-swarm system is presented.
https://research.utwente.nl/en/publications/the-quadratic-0-1-knapsack-problem-with-series-parallel-support
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.Cited by: 59
https://core.ac.uk/display/11478228
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.Author: David J. Rader Jr and Gerhard J. Woeginger
https://www.narcis.nl/publication/RecordID/oai%3Apure.tue.nl%3Apublications%2F8f9cb5a4-7e51-4173-a7e1-6b782d412e15
The quadratic 0-1 knapsack problem with series-parallel support (2002) Pagina-navigatie: Main; Save publication. Save as MODS; Export to Mendeley; Save as EndNote; Export to RefWorks; Title: The quadratic 0-1 knapsack problem with series-parallel support: Published in: Operations Research Letters, Vol. 30, No. 3, p.159-166. ISSN 0167-6377 ...Cited by: 59
http://www.optimization-online.org/DB_FILE/2013/12/4167.pdf
maximum clique problem can be reduced to it: Given a graph G, we set wj = 1 and p j = 0 for all j and assign profits p ij = 1 for all (i,j) ∈ E. Solving QKP with c = k, it follows that G contains a clique of size k iff the optimal solution
https://www.sciencedirect.com/science/article/pii/S0167637716300323
The quadratic knapsack problem (QKP) can be defined in graph theoretic terms as follows. Let G be a graph with vertices vi,i=1,…,n with costs ci≥0 associated with the vertices and profitspij≥0 associated with each edge ij and each vertex i (corresponding to pii).Cited by: 5
https://www.deepdyve.com/lp/elsevier/the-quadratic-knapsack-problem-a-survey-Mh7kcv40AJ
Mar 15, 2007 · The quadratic knapsack problem—a survey Pisinger, David 2007-03-15 00:00:00 The binary quadratic knapsack problem maximizes a quadratic objective function subject to a linear capacity constraint. Due to its simple structure and challenging difficulty it has been studied intensively during the last two decades.Author: Pisinger, David
https://www.researchgate.net/publication/281607673_On25_Approximation_of_the_Quadratic_Knapsack_Problem
After solving the knapsack problem with two constraints, it is equivalently replaced by a combination of the two knapsack problems with one constraint each.
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