Average-case analyses of first fit and random fit bin packing. Random Structures Algorithms

We prove that the First Fit bin packing algorithm is stable under the input distribution Ufk 2; kg for all k 3, settling an open question from the recent survey by Coman, 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 [10]. 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 Ufk 2; kg, as well as present worst-case bounds and some results on distributions Ufk 1; kg and Ufk; kg for Random Fit.