Hassene Aissi

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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 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)
This paper investigates, for the first time in the literature, the approximation of minmax (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)
We present in this paper general pseudo-polynomial time algorithms to solve min-max and min-max regret versions of some polynomial or pseudo-polynomial problems under a constant number of scenarios. Using easily computable bounds, we can improve these algorithms. This way we provide pseudo-polynomial algorithms for the min-max and and min-max regret(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 general approximation schemes which can be used for min-max and min-max regret versions of some polynomial or(More)