Robust Monotone Submodular Function Maximization

• Main Authors: Orlin, James B (Author), Schulz, Andreas S (Author), Udwani, Rajan (Author)
• Other Authors: Sloan School of Management (Contributor)
• Format: Article
• Language: English
• Published: Springer International Publishing, 2021-01-27T21:55:17Z.
• Subjects: Article
• Online Access: Get fulltext

Part of the Lecture Notes in Computer Science book series (LNCS, volume 9682)
We consider a robust formulation, introduced by Krause et al. (2008), of the classic cardinality constrained monotone submodular function maximization problem, and give the first constant factor approximation results. The robustness considered is w.r.t. adversarial removal of a given number of elements from the chosen set. In particular, for the fundamental case of single element removal, we show that one can approximate the problem up to a factor (1−1/e)−ϵ by making O(n 1/ϵ) queries, for arbitrary ϵ > 0. The ideas are also extended to more general settings.