FPTAS for half-products minimization with scheduling applications

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...

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Bibliographic Details
Published in:Discrete Applied Mathematics Vol. 156; no. 15; pp. 3046 - 3056
Main Authors: Erel, Erdal, Ghosh, Jay B.
Format: Journal Article
Language:English
Published: Lausanne Elsevier B.V 06.08.2008
Amsterdam Elsevier
New York, NY
Subjects:
Algorithmics. Computability. Computer arithmetics
Applied sciences
Approximation scheme
Combinatorics
Combinatorics. Ordered structures
Computer science; control theory; systems
Computer systems performance. Reliability
Dynamic programming
Exact sciences and technology
Mathematics
Order, lattices, ordered algebraic structures
Quadratic pseudo-boolean functions
Sciences and techniques of general use
Software
Theoretical computing
Approximation scheme
Quadratic pseudo-boolean functions
Dynamic programming
Computer theory
Polynomial approximation
Boolean function
Minimization
Product
Scheduling
Optimization
Polynomial time
Combinatorics
Application
Quadratic function
ISSN:0166-218X, 1872-6771
Online Access:Get full text
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Summary: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.
ISSN:0166-218X
1872-6771
DOI:10.1016/j.dam.2008.01.018