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Min-max and min-max regret criteria are commonly used to define robust solutions. After motivating the use of these criteria, we present general results. Then, we survey complexity results for the min-max and min-max regret versions of some combinatorial optimization problems: shortest path, spanning tree, assignment, min cut, min s-t cut, knapsack. Since(More)
While the complexity of min-max and min-max regret versions of most classical combinatorial optimization problems has been thoroughly investigated, there are very few studies about their approximation. For a bounded number of scenarios, we establish a general approximation scheme which can be used for min-max and min-max regret versions of some polynomial(More)
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 constant number of scenarios, we establish fully polynomial-time approximation schemes for the min-max versions of these problems, using relationships between(More)
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(More)
This paper investigates the complexity of the min-max and min-max regret versions of the s − t min cut and min cut problems. Even if the underlying problems are closely related and both polynomial, we show that the complexity of their min-max and min-max regret versions , for a constant number of scenarios, are quite contrasted since they are respectively(More)
While the complexity of min-max and min-max regret versions of most classical com-binatorial optimization problems has been thoroughly investigated, there are very few studies about their approximation. For a bounded number of scenarios, we establish general approximation schemes which can be used for min-max and min-max regret versions of some polynomial(More)
This paper investigates the complexity of the min-max and min-max regret versions of the min s-t cut and min cut problems. Even if the underlying problems are closely related and both polynomial, the complexity of their min-max and min-max regret versions, for a constant number of scenarios, is quite contrasted since they are respectively strongly NP-hard(More)