  Robust optimization is a widely studied area in operations research, where
the algorithm takes as input a range of values and outputs a single solution
that performs well for the entire range. Specifically, a robust algorithm aims
to minimize regret, defined as the maximum difference between the solution's
cost and that of an optimal solution in hindsight once the input has been
realized. For graph problems in P, such as shortest path and minimum spanning
tree, robust polynomial-time algorithms that obtain a constant approximation on
regret are known. In this paper, we study robust algorithms for minimizing
regret in NP-hard graph optimization problems, and give constant approximations
on regret for the classical traveling salesman and Steiner tree problems.
