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Approximation schemes for quadratic Boolean programming problems and their scheduling applications

Approximation schemes for quadratic Boolean programming problems and their scheduling applications

Strusevich, Vitaly A. and Kellerer, Hans (2013) Approximation schemes for quadratic Boolean programming problems and their scheduling applications. In: OR55 Annual Conference - Keynote Papers and Extended Abstracts. Operational Research Society Limited, Birmingham, UK, pp. 73-85. ISBN 0903440555

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Abstract

We consider Boolean programming problems with quadratic objective functions, related to the Half-Product introduced by Badics and Boros in 1998. The variants include problems of minimizing the Half-Product with an additive constant, convex positive Half-Product, a symmetric quadratic function, with and without a linear knapsack constraint. A methodology for designing fully polynomial-time approximation schemes (FPTASs) for these problems is presented. As one of the prerequisites for designing an FPTAS, the problem at hand must admit a constant-ratio approximation algorithm. We develop such algorithms by solving the continuous relaxation of a Boolean programming problem in strongly polynomial time followed by an appropriate rounding of the fractional variables. The problems under consideration serve as mathematical programming reformulations of a wide range of scheduling problems with mini-sum objective functions. The corresponding FPTASs can be adapted to be applicable to these scheduling problems.

Item Type: Conference Proceedings
Title of Proceedings: OR55 Annual Conference - Keynote Papers and Extended Abstracts
Additional Information: [1] This Keynote paper was first presented at the OR 55 Annual Conference held from 3-5 September 2013 in Exeter, UK. And the full-text of the keynote conference paper is held on GALA with permission from the publisher.
Uncontrolled Keywords: quadratic boolean programming, approximation, scheduling
Subjects: Q Science > QA Mathematics
Faculty / Department / Research Group: Faculty of Architecture, Computing & Humanities
Related URLs:
Last Modified: 14 Oct 2016 09:28
Selected for GREAT 2016: None
Selected for GREAT 2017: None
Selected for GREAT 2018: None
URI: http://gala.gre.ac.uk/id/eprint/12197

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