Submitted to 2001 ACM - SIAM Symp . on Discrete Algorithms Better Approximation Algorithms for Bin

Bin covering takes as input a list of item sizes and places them into bins of unit demand so as to maximize the number of bins whose demand is satissed. This is in a sense a dual problem to the classical one-dimensional bin packing problem, but has for many years lagged behind the latter as far as the quality of the best approximation algorithms. We design algorithms for this problem that close the gap, both in terms of worst-and average-case results. We present (1) the rst approximation scheme for the ooine version, (2) algorithms with bounded worst-case behavior whose expected behavior is asymptotically optimal for all discrete \perfect-packing distributions" (ones for which optimal packings have sublinear expected waste), and (3) a learning algorithm that has asymptotically optimal expected behavior for all discrete distributions. The algorithms of (2) and (3) are based on the recently-developed online Sum-of-Squares algorithm for bin packing, whose adaptation to the case of bin covering requires new ideas and analytical techniques. We also present experimental analysis comparing the algorithms of (2) and suggesting that one of them, the Sum-of-Squares-with-Threshold algorithm, performs quite well even for discrete distributions that do not have the perfect-packing property.