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.

稳健优化是运筹学中广泛研究的领域，其中算法将一系列值作为输入，并输出在整个范围内表现良好的单一解决方案。具体来说，一个稳健的算法旨在最大限度地减少后悔，定义为解决方案的成本与实现输入后的事后最佳解决方案之间的最大差异。对于P中的图形问题，例如最短路径和最小生成树，获得对后悔的常数近似的鲁棒多项式时间算法是已知的。在本文中，我们研究了在NP难图优化问题中最小化遗憾的鲁棒算法，并给出了经典旅行商和斯坦纳树问题的遗憾的常数近似值。