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Vietnam Journal of Mathematics 35:4(2007)
373-386
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Admissible Transformations and Assignment
Problems
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Rainer E. Burkard
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Abstract. We introduce the notion of admissible
transformations which is related to the Hungarian method for solving
assignment problems. Admissible transformations are stated for linear,
quadratic and multi-index assignment problems. Their application to find
good lower bounds and/or to solve the problem, respectively, is outlined.
Finally it is shown that admissible transformations can also be applied to
so-called algebraic objective functions whose cost elements are drawn from
a totally ordered semigroup.
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Keywords: Combinatorial optimization, assignment
problems, quadratic assignment problem, multi-index assignment problem,
admissible transformation, algebraic optimization.
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Established
by Vietnam Academy of Science and Technology & Vietnam Mathematical
Society
Published
by Springer since January 2013
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