对抗注入下的鲁棒算法
Robust Algorithms under Adversarial Injections
摘要：
在本文中，我们研究的背景下，在输入的随机性流和在线算法。对于几个问题，输入序列的随机顺序-与最坏情况的顺序相反-似乎是一个必要的邪恶，以证明令人满意的保证。然而，在这种假设下工作的算法技术往往容易受到分布中即使很小的变化的影响。为此，我们提出了一个新的\emph{adversarial injections}模型，其中输入是随机排序的，但对手可能会在任意位置注入误导性元素。我们相信，在这个弱得多的假设下研究算法可以带来新的见解，特别是更强大的算法。在这个模型中，我们研究了两个经典的组合优化问题：最大匹配和基数约束单调子模函数最大化。我们的主要技术贡献是一种新的流算法，后者计算一个$0.55$近似。虽然该算法本身是干净和简单的，但相关的分析表明，它模拟了输入流的细分，可以用来大大限制对手的力量。
英文摘要：
In this paper, we study streaming and online algorithms in the context of randomness in the input. For several problems, a random order of the input sequence---as opposed to the worst-case order---appears to be a necessary evil in order to prove satisfying guarantees. However, algorithmic techniques that work under this assumption tend to be vulnerable to even small changes in the distribution. For this reason, we propose a new \emph{adversarial injections} model, in which the input is ordered randomly, but an adversary may inject misleading elements at arbitrary positions. We believe that studying algorithms under this much weaker assumption can lead to new insights and, in particular, more robust algorithms. We investigate two classical combinatorial-optimization problems in this model: Maximum matching and cardinality constrained monotone submodular function maximization. Our main technical contribution is a novel streaming algorithm for the latter that computes a $0.55$-approximation. While the algorithm itself is clean and simple, an involved analysis shows that it emulates a subdivision of the input stream which can be used to greatly limit the power of the adversary.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
