Note: FPTAS for half-products minimization with scheduling applications

Authors:
Erdal Erel;Jay B. Ghosh
Affiliations:
Faculty of Business Administration, Bilkent University, 06800 Bilkent, Ankara, Turkey;Korea University Business School, Korea University, Seoul, Korea
Venue:
Discrete Applied Mathematics
Year:
2008

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Abstract

A special class of quadratic pseudo-boolean functions called ''half-products'' (HP) has recently been introduced. It has been shown that HP minimization, while NP-hard, admits a fully polynomial time approximation scheme (FPTAS). In this note, we provide a more efficient FPTAS. We further show how an FPTAS can also be derived for the general case where the HP function is augmented by a problem-dependent constant and can justifiably be assumed to be nonnegative. This leads to an FPTAS for certain partitioning type problems, including many from the field of scheduling.