In the well known planted clique problem, a clique (or alternatively, an independent set) of size k is planted at random in an Erdos-Renyi random G(n, p) graph, and the goal is to design an algorithm that finds the maximum clique (or independent set) in the resulting graph. We introduce a variation on this problem, where instead of planting the clique at random, the clique is planted by an adversary who attempts to make it difficult to find the maximum clique in the resulting graph. We show that for the standard setting of the parameters of the problem, namely, a clique of size \(k = \sqrt{n}\) planted in a random \(G(n, \frac{1}{2})\) graph, the known polynomial time algorithms can be extended (in a non-trivial way) to work also in the adversarial setting. In contrast, we show that for other natural settings of the parameters, such as planting an independent set of size \(k=\frac{n}{2}\) in a G(n, p) graph with \(p = n^{-\frac{1}{2}}\), there is no polynomial time algorithm that finds an independent set of size k, unless NP has randomized polynomial time algorithms.

在众所周知的种植派问题中，大小为k的派（或者独立集）被随机种植在 Erdos-Renyi 随机G ( n ,  p ) 图中，目标是设计一种算法来找到结果图中的最大集团（或独立集）。我们引入了这个问题的一个变体，其中不是随机植入派系，而是由对手植入派系，该对手试图使在结果图中找到最大派系变得困难。我们证明，对于问题参数的标准设置，即在随机的\(G(n, \frac{1}{2})中种植一个大小为\(k = \sqrt{n}\)的团\)图，已知的多项式时间算法可以扩展（以一种不平凡的方式）以在对抗性设置中也能工作。相比之下，我们表明对于参数的其他自然设置，例如在G ( n ,  p ) 图中种植一组独立的大小\(k=\frac{n}{2}\)且\(p = n^{-\frac{1}{2}}\)，没有多项式时间算法可以找到大小为k的独立集合，除非 NP 有随机多项式时间算法。