  In two-stage robust optimization the solution to a problem is built in two
stages: In the first stage a partial, not necessarily feasible, solution is
exhibited. Then the adversary chooses the "worst" scenario from a predefined
set of scenarios. In the second stage, the first-stage solution is extended to
become feasible for the chosen scenario. The costs at the second stage are
larger than at the first one, and the objective is to minimize the total cost
paid in the two stages.
  We give a 2-approximation algorithm for the robust mincut problem and a
({\gamma}+2)-approximation for the robust shortest path problem, where {\gamma}
is the approximation ratio for the Steiner tree. This improves the factors
(1+\sqrt2) and 2({\gamma}+2) from [Golovin, Goyal and Ravi. Pay today for a
rainy day: Improved approximation algorithms for demand-robust min-cut and
shortest path problems. STACS 2006]. In addition, our solution for robust
shortest path is simpler and more efficient than the earlier ones; this is
achieved by a more direct algorithm and analysis, not using some of the
standard demand-robust optimization techniques.
