In this paper, we present an O(n1ogn) algorithm to compute a tighter lower bound for the one-dimensional bin packing problem. We have simulated the algorithm on randomly generated bin packing problems with item sizes drawn uniformly from (a, b], where 0 5 a < b 5 B and B is bin size. Using our lower bound, the average error of BFD is less than 2%. For a + b > B, the error is less than 0.003%.


bin packing, lower bound, best fit decreasing, harmonic partition, matching

Date of this Version

June 1995