Before revision:  Previously, a randomized approximation algorithm obtained a (1 - 1/ e-\epsilon) approximation ratio based on the involved continuous greedy technique. We then generalize the result to arbitrary number of bins. When the capacity of bins are identical, we design a combinatorial and deterministic algorithm which achieves an almost tight approximation ratio (1 - 1 / e-\epsilon). In the general case, we provide a (1/2-\epsilon)-approximation algorithm which is also combinatorial and deterministic . We finally boost this algorithmto a (1-1/e-\epsilon) randomized algorithm for the general case, thus matching the result of Fairstein et al. 13 .
After revision:  Previously, a randomized approximation algorithm obtained a (1 - 1/ e-\epsilon) 13 .