论文标题
如何隐藏一个集团？
How to hide a clique?
论文作者
论文摘要
在众所周知的种植集团问题中，在Erdos-Renyi Random $ G（N，P）$图中随机种植了一个大小$ K $的集团（或独立的集合），其目标是设计一种算法，该算法在结果图中找到最大的集合（或独立集）。我们引入了关于这个问题的变化，在该问题中，该集团不是随机种植该集团，而是由一个试图使最大值的敌人在结果图中找到最大集团的植物。我们表明，对于问题的参数的标准设置，即，在随机的$ g（n，\ frac {1} {2}）$中种植的大小$ k = \ sqrt {n} $的集团，可以扩展（在非trivial的方式中），以在advesrial设置中，可以扩展已知的多项式时间算法。 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时间算法。
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.
