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Ante Custic(custicopt.math.tugraz.at) Abstract: Given a combinatorial optimization problem, we aim at characterizing the set of all instances for which every feasible solution has the same objective value. Our central result deals with multidimensional assignment problems. We show that for the axial and for the planar $d$dimensional assignment problem instances with constant objective value property are characterized by sumdecomposable arrays. We provide a counterexample to show that the result does not carry over to general $d$dimensional assignment problems. Our result for the axial $d$dimensional assignment problems can be shown to carry over to the axial $d$dimensional transportation problem. Moreover, we obtain characterizations when the constant objective value property holds for the minimum spanning tree problem, the shortest path problem and the minimum weight maximum cardinality matching problem. Keywords: Constant objective value; admissible transformation; multidimensional assignment problem; sumdecomposable array. Category 1: Combinatorial Optimization Citation: Download: [PDF] Entry Submitted: 05/21/2014 Modify/Update this entry  
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