Bin covering problem

In the bin covering problem, items of different sizes must be packed into a finite number of bins or containers, each of which must contain at least a certain given total size, in a way that maximizes the number of bins used.

This problem is a dual of the bin packing problem: in bin covering, the bin sizes are bounded from below and the goal is to maximize their number; in bin packing, the bin sizes are bounded from above and the goal is to minimize their number.

The problem is NP-hard, but there are various efficient approximation algorithms:

• Algorithms covering at least 1/2, 2/3 or 3/4 of the optimum bin count asymptotically, running in time ${\displaystyle O(n),O(n\log n),O(n{\log }^{2}n)}$ respectively.
• An asymptotic PTAS, algorithms with bounded worst-case behavior whose expected behavior is asymptotically-optimal for some discrete distributions, and a learning algorithm with asymptotically optimal expected behavior for all discrete distributions.
• An asymptotic FPTAS.