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

Susanne Albers, Michael Mitzenmacher
2000 Random structures & algorithms (Print)  
We prove that the First Fit bin packing algorithm is stable under the input distribution U fk 2; kg for all k 3, settling an open question from the recent survey by Co man, 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
more » ... own right. We show that Random Fit is stable under the input distributions U fk 2; kg, as well as present worst-case bounds and some results on distributions U fk 1; kg and U fk; kg for Random Fit.
doi:10.1002/(sici)1098-2418(200005)16:3<240::aid-rsa2>3.0.co;2-v fatcat:oel6gtr5w5cnzb52w6ttypeghq