Average-case analyses of first fit and random fit bin packing (1998) [13 citations — 2 self]
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by Susanne Albers, Michael Mitzenmacher
In Proc. Ninth Annual ACM-SIAM Symposium on Discrete Algorithms
http://www.mpi-sb.mpg.de/~albers/soda98.ps.gz
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Abstract:
We prove that the First Fit bin packing algorithm is stable under the input distribution Ufk \Gamma 2; kg 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 [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 \Gamma 2; kg, as well as present worst-case bounds and some results on distributions Ufk \Gamma 1; kg and Ufk; kg for Random Fit. 1
