Optimal Bin Covering with Items of Random Size

Consider a probability measure $\mu $ on $[0,1]$ and independent random variables $X_1 , \cdots ,X_n $ distributed according to $\mu $. Let $Q_n = Q_n (X_1 , \cdots ,X_n )$ be the largest number of unit-size bins that can be covered by items of size $X_1 , \cdots ,X_n $. The properties of $Q_n $ are investigated in the spirit of our work on optimal bin packing with items of random sizes. While the covering problem has many similarities with the packing problem, it turns out to be significantly harder.