Complexity of the min-max (regret) versions of min cut problems

Authors:
Hassene Aissi;Cristina Bazgan;Daniel Vanderpooten
Affiliations:
LAMSADE, Université Paris-Dauphine, France;LAMSADE, Université Paris-Dauphine, France;LAMSADE, Université Paris-Dauphine, France
Venue:
Discrete Optimization
Year:
2008

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Abstract

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 complexities of their min-max and min-max regret versions, for a constant number of scenarios, are quite contrasted since they are respectively strongly NP-hard and polynomial. However, for a non-constant number of scenarios, these versions become strongly NP-hard for both problems. In the interval scenario case, min-max versions are trivially polynomial. Moreover, for min-max regret versions, we obtain the same contrasted results as for a constant number of scenarios: min-max regret min s-t cut is strongly NP-hard whereas min-max regret min cut is polynomial.