We show that the greedy algorithm for adaptive-submodular cover has approximation ratio at least 1.3*(1+ln Q). Moreover, the instance demonstrating this gap has Q=1. So, it invalidates a prior result in the paper ``Adaptive Submodularity: A New Approach to Active Learning and Stochastic Optimization'' by Golovin-Krause, that claimed a (1+ln Q)^2 approximation ratio for the same algorithm.
翻译:我们证明自适应子模覆盖问题的贪心算法近似比至少为1.3*(1+ln Q)。此外,证明该差距的实例中Q=1。因此,这推翻了Golovin-Krause论文《Adaptive Submodularity: A New Approach to Active Learning and Stochastic Optimization》中关于同一算法具有(1+ln Q)^2近似比的原有结论。