Goemans and Williamson proposed a randomized rounding algorithm for the MAX-CUT problem with a 0.878 approximation bound in expectation. The 0.878 approximation bound remains the best-known approximation bound for this APX-hard problem. Their approach was subsequently applied to other related problems such as Max-DiCut, MAX-SAT, and Max-2SAT, etc. We show that the randomized rounding algorithm can also be used to achieve a 0.878 approximation bound for the robust and distributionally robust counterparts of the max-cut problem. We also show that the approximation bounds for the other problems are maintained for their robust and distributionally robust counterparts if the randomization projection framework is used.

翻译：Goemans和Williamson提出了一种针对MAX-CUT问题的随机舍入算法，其期望近似比达到0.878。对于这一APX难问题，0.878的近似比界仍是目前已知的最佳结果。他们的方法随后被应用于其他相关问题，如Max-DiCut、MAX-SAT和Max-2SAT等。本文证明，该随机舍入算法同样可用于在最大割问题的鲁棒版本及分布鲁棒版本上实现0.878的近似比。我们进一步表明，若采用随机投影框架，其他相关问题的近似比界在其鲁棒及分布鲁棒版本中同样得以保持。