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Improved dynamic programming and approximation results for the knapsack problem with setups

Ulrich Pferschy(pferschy***at***uni-graz.at)
Rosario Scatamacchia(d021123***at***polito.it)

Abstract: We consider the 0-1 Knapsack Problem with Setups (KPS). Items are grouped into families and if any items of a family are packed, this induces a setup cost as well as a setup resource consumption. We introduce a new dynamic programming algorithm which performs much better than a previous dynamic program and turns out to be also a valid alternative to an exact approach based on the use of an ILP solver. Then we present a general inapproximability result. Furthermore, we investigate several relevant special cases which still permit fully polynomial time approximation schemes (FPTASs) and others where the problem remains hard to approximate.

Keywords: knapsack problem, setup cost, dynamic programming, approximability

Category 1: Combinatorial Optimization

Category 2: Integer Programming (0-1 Programming )

Category 3: Combinatorial Optimization (Approximation Algorithms )


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Entry Submitted: 07/12/2016
Entry Accepted: 07/12/2016
Entry Last Modified: 07/12/2016

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