This paper deals with the max-min and min-max regret versions of the maximum
weighted independent set problem on interval graphswith uncertain vertex
weights. Both problems have been recently investigated by Nobibon and Leus
(2014), who showed that they are NP-hard for two scenarios and strongly NP-hard
if the number of scenarios is a part of the input. In this paper, new
complexity and approximation results on the problems under consideration are
provided, which extend the ones previously obtained. Namely, for the discrete
scenario uncertainty representation it is proven that if the number of
scenarios K is a part of the input, then the max-min version of the problem
is not at all approximable. On the other hand, its min-max regret version is
approximable within K and not approximable within O(log1−ϵK) for
any ϵ>0 unless the problems in NP have quasi polynomial algorithms.
Furthermore, for the interval uncertainty representation it is shown that the
min-max regret version is NP-hard and approximable within 2