General approximation schemes for min-max (regret) versions of some (pseudo-)polynomial problems

Authors:
Hassene Aissi;Cristina Bazgan;Daniel Vanderpooten
Affiliations:
Université Paris-Dauphine, LAMSADE, Place du Maréchal de Lattre de Tassigny, 75775 Paris Cedex 16, France;Université Paris-Dauphine, LAMSADE, Place du Maréchal de Lattre de Tassigny, 75775 Paris Cedex 16, France;Université Paris-Dauphine, LAMSADE, Place du Maréchal de Lattre de Tassigny, 75775 Paris Cedex 16, France
Venue:
Discrete Optimization
Year:
2010

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Abstract

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 pseudo-polynomial problems. Applying these schemes to shortest path, minimum spanning tree, minimum weighted perfect matching on planar graphs, and knapsack problems, we obtain fully polynomial-time approximation schemes with better running times than the ones previously presented in the literature.