Improved approximations for robust mincut and shortest path

TL;DR

This paper presents improved approximation algorithms for two-stage robust mincut and shortest path problems, achieving better approximation ratios and simpler, more efficient solutions compared to previous methods.

Contribution

It introduces a 2-approximation for robust mincut and a ({rac}{}{}+2)-approximation for robust shortest path, enhancing previous bounds with a more straightforward approach.

Findings

Achieved a 2-approximation for robust mincut.

Developed a ({rac}{}{}+2)-approximation for robust shortest path.

Provided simpler and more efficient algorithms than earlier methods.

Abstract

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.