Average-case analysis of first fit and random fit bin packing

We prove that the First Fit bin packing algorithm is stable under the input distribution U{k − 2, k} for all k ≥ 3, settling an open question from the recent survey by Coffman, Garey, and Johnson [3]. Our proof generalizes the multi-dimensional Markov chain analysis used by Kenyon, Rabani, and Sinclair to prove that Best Fit is also stable under these distributions [11]. Our proof is motivated by an analysis of Random Fit, a new simple packing algorithm related to First Fit, that is interesting in its own right. We show that Random Fit is stable under the input distributions U{k − 2, k}, as well as present worst-case bounds and some results on distributions U{k − 1, k} and U{k, k} for Random Fit.