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Knapsack problems
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Duality theorems for marginal problems
SummaryGiven topological spaces X1, ..., Xn with product space X, probability measures μi on Xi together with a real function h on X define a marginal problem as well as a dual problem. Using an…
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Introduction to NP-Completeness of Knapsack Problems
The reader may have noticed that for all the considered variants of the knapsack problem, no polynomial time algorithm have been presented which solves the problem to optimality. Indeed all the…
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Approximation algorithms for knapsack problems with cardinality constraints
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Parallel machine scheduling with job assignment restrictions
TLDR
An algorithm is contributed that provides a 3/2 worst case bound and runs in time linear in the number of jobs for assignment restrictions determined by just one characteristic of the machines.
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Semi on-line algorithms for the partition problem
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Optimization of cardinality constrained portfolios with a hybrid local search algorithm
TLDR
This paper suggests a hybrid local search algorithm which combines principles of Simulated Annealing and evolutionary strategies and which proved to highly efficiently approach this problem.
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A New Fully Polynomial Time Approximation Scheme for the Knapsack Problem
TLDR
A fully polynomial time approximation scheme (FPTAS) is presented for the classical 0-1 knapsack problem, which considerably improves the necessary space requirements and reduces the running time.
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An efficient fully polynomial approximation scheme for the Subset-Sum Problem
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A PTAS for the Multiple Subset Sum Problem with different knapsack capacities
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