Better approximation algorithms for bin covering

Bin covering takes as input a list of items with sizes in (0 1) and places them into bins of unit demand so as to maximize the number of bins whose demand is satis ed. 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 in terms of 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 asymptotic approximation scheme for the o ine version, (2) algorithms that have bounded worst-case behavior for instances with discrete item sizes and expected behavior that 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...

• Type: Conference
• Year: 2001
• Where: SODA
• Authors: János Csirik, David S. Johnson, Claire Kenyon
• Keywords: Algorithms, Bin Packing, Discrete Distributions, SODA 2001