How to pack better than best fit: tight bounds for average-case online bin packing

An O(n log n)-time online algorithm is given for packing items i.i.d. uniform on [0, 1] into bins of size 1 with expected wasted space Θ(n^1/2 log ^1/2 n). This matches the lowest bound that no online algorithm can achieve O(n^1/2 log ^1/2 n) wasted space. It is done by analyzing another algorithm which involves putting balls into buckets online. The analysis of this second algorithm also gives bound on the stochastic rightward matching problem, which arises in analyzing not only the above online bin packing problem, but also a 2-D problem of packing rectangles into a half-infinite strip. The bounds on rightward matching thus give good bounds for the 2-D strip packing problem