Fully Polynomial Approximation Schemes for a Symmetric Quadratic Knapsack Problem and its Scheduling Applications

Authors:
Hans Kellerer;Vitaly A. Strusevich
Affiliations:
Universität Graz, Institut für Statistik und Operations Research, Universitätsstraße 15, 8010, Graz, Austria;University of Greenwich, Old Royal Naval College, School of Computing and Mathematical Sciences, Park Row, Greenwich, SE10 9LS, London, UK
Venue:
Algorithmica
Year:
2010

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Abstract

We design a fully polynomial-time approximation scheme (FPTAS) for a knapsack problem to minimize a symmetric quadratic function. We demonstrate how the designed FPTAS can be adopted for several single machine scheduling problems to minimize the sum of the weighted completion times. The applications presented in this paper include problems with a single machine non-availability interval (for both the non-resumable and the resumable scenarios) and a problem of planning a single machine maintenance period; the latter problem is closely related to a single machine scheduling problem with two competing agents. The running time of each presented FPTAS is strongly polynomial.