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2005
Springer

Approximation Complexity of min-max (Regret) Versions of Shortest Path, Spanning Tree, and Knapsack

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Approximation Complexity of min-max (Regret) Versions of Shortest Path, Spanning Tree, and Knapsack
This paper investigates, for the first time in the literature, the approximation of min-max (regret) versions of classical problems like shortest path, minimum spanning tree, and knapsack. For a bounded number of scenarios, we establish fully polynomial-time approximation schemes for the min-max versions of these problems, using relationships between multi-objective and min-max optimization. Using dynamic programming and classical trimming techniques, we construct a fully polynomial-time approximation scheme for min-max regret shortest path. We also establish a fully polynomial-time approximation scheme for minmax regret spanning tree and prove that min-max regret knapsack is not at all approximable. We also investigate the case of an unbounded number of scenarios, for which min-max and min-max regret versions of polynomial-time solvable problems usually become strongly NP-hard. In this setting, non-approximability results are provided for min-max (regret) versions of shortest path an...
Hassene Aissi, Cristina Bazgan, Daniel Vanderpoote
Added 29 Jun 2010
Updated 29 Jun 2010
Type Conference
Year 2005
Where ESA
Authors Hassene Aissi, Cristina Bazgan, Daniel Vanderpooten
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